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Trig/Math Anal
Name_______________________No_____
LATE AND ABSENT HOMEWORK IS ACCEPTED UP TO THE TIME OF THE CHAPTER TEST ON _____
HW NO.
PS-1
PS-2
PS-3
SECTIONS
Fundamental
Counting and
Permutations
16-1/16-2/16-3
Combinations
16-4
Sample Spaces
and Probability
16-5/16-6
ASSIGNMENT
DUE
√
Practice Set A/3-10
Practice Set B/1-14
Practice Set C/1-9 odd
Practice Set D/11-19 odd, 21-24, 26
Practice Set K/3, 4, 5, 10, 11, 17-22, 25
Practice Set E/1-4, 6-8
Practice Set F/1-10
PS-4
Mutually
Exclusive and
Independent
Events
16-7
Practice Set G/1-16
PS-5
Review
Practice Set L/1-9
Practice Set M/1-8
Practice Set A: Fundamental Counting Principles (Page 719)
1. On a bookshelf there are 10 different algebra books, 6 different geometry books, and 4
different calculus books. In how many ways can you choose 3 books, one of each kind?
2. In how many different ways can a 10 question true-false test be answered if each question
must be answered?
3. In how many ways can a 10-question true-false test be answered if it is permissible to leave
questions unanswered?
4. How many ways are there of selecting 3 cards, one after the other, from a deck of 26 cards if
selected cards are not returned to the deck?
5. A student council has 6 seniors, 5 juniors, and 1 sophomore as members. In how many ways
can a 3-member council committee be formed that includes one member of each class?
6. How many license plates of 5 symbols can be made using a letter for the first symbol and
digits for the remaining 4 symbols?
7. How many 4-digit telephone numbers can be formed if each digit is greater than or equal to
3?
8. In how many ways can a person make a sandwich if there are 5 choices of meat and 4 choices
of bread?
9. How many positive odd integers containing 3 digits can be formed using the digits 5, 6, 7, 8,
and 9?
10. How many positive odd integers, having at most 3 digits can be formed using the digits 5, 6,
7, 8, and 9?
11. How many positive odd integers less than 100 can be formed using the digits 5, 6, 7, and 8?
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12. How many positive odd integers less than 10,000 can be formed using the digits 3, 4, 6, 8,
and 0?
13. How many positive odd integers between 100 and 10,000 can be formed using the digits 2, 3,
4, 5, and 6?
14. How many license plates of 3 symbols (letters and digits) can be made using at least 2 letters
for each?
15. How many multiples of 3 less than 100 can be formed from the digits 1, 4, 5, 7, and 8? (Hint:
The sum of the digits of any multiple of 3 is also a multiple of 3).
16. How many multiples of 3 less than 1000 can be formed from the digits 2, 5, and 9?
17. You have totally forgotten the combination to your locker, which has three numbers in
sequence (right, left, right). Each number is between 0 and 35. If you can test one combination
every 15 seconds, how long will it take you to test all possible combinations?
18. DNA (deoxyribonucleic acid) molecules include the base units adenine, thymine, cytosine,
and guanine (A, T, C, and G). The sequence of base units along a strand of DNA encodes genetic
information. In how many different sequences can the 4 base units A, T, C, and G be arranged
along a short strand of DNA that includes only 8 base units?
19. Protein molecules are made up of many amino acid residues joined end-to-end. Proteins
have different properties, depending on the sequence of amino acid residues in the molecules. If
there are 20 naturally occurring amino acids, how many different sequences of amino acid
residues can occur in a 4-residue-long fragment of a protein molecule?
20. How many 3-letter code words can be formed if at least one of the letters is to be chosen
from the vowels a, e, i, o, and u?
Practice Set B: Permutations (Page 723)
Evaluate each of the following.
6!
2.  4! 3!
3. 4  3!
 20!
1.
4.
2!4!
 20  3!
Find n Pr for each pair of values of n and r .
5. n  5, r  2
6. n  10, r  10
7. n  6, r  3
8. n  6, r  2
9. In how many ways can you arrange 5 different books on a shelf?
10. In how many ways can 4 people be lined up in a row for a photograph?
11. In how many ways can the letters of the word MONDAY be arranged using all 6 letters?
12. In how many ways can the letters of the word EIGHT be arranged using only 4 of the letters
at a time?
13. How many positive integers between 999 and 5000 can be formed using the digits 2, 3, 4, 5,
6, and 7 if no digit may be repeated?
14. How many positive integers less than 1000 can be formed using the digits 1, 2, 3, 4, and 5 if
no digit may be repeated?
15. Show that 7 P4  7  6 P3 
16. Show that 6 Pr  6  5 Pr 1 
17. Show that n P5  n  n1 P4 
18. Show that 5 P3 5 P2  2  5 P2 
19. Show that n P5 n P4   n  5n P4
20. Show that n Pr n Pr 1   n  r n Pr 1
21. Solve for n : n P5  14  n P4 
22. Solve for n : n P3  17  n P2 
Practice Set C: Permutations with Repeated Elements (Page 726)
Find the number of permutations of all the letters in each word.
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1. TRIGGER
2. ROTOR
3. MISSISSIPPI 4. DEEDED
5. INDIANA
6. CINCINNATI
7. How many different signals can be made by displaying five flags all at a time, on a flagpole?
The flags differ only in color; two are red, two are black, and one is blue.
8. How many different signals could be made if the flags of Exercise 7 were of the following
colors: three red, one black, and one blue?
9. In how many ways can 3 identical emeralds, 2 identical diamonds, and 2 identical opals be
arranged in a row in a display case?
10. In how many ways can 3 red, 4 blue, and 2 green pens be distributed among 9 students
seated in a row if each student receives one pen?
How many five-digit integers can be made in each case?
11. 3, 5, and 6 may each be used once; 8 may be used twice.
12. 1 and 2 may each be used twice; 3 may be used once.
13. 5 may be used three times; 4 may be used twice.
14. Find the number of 6-letter permutations that can be formed from the letters in the word
SHOPPER.
Practice Set D: Combinations (Page 729)
1. For the 3-letter set K , L, M  , specify:
a) all the subsets
b) the subsets containing at least 2 letters
2. For the 4-digit set 2, 4,6,8 , specify:
a) the 2-digit subsets
b) the subsets in which the sum of the digits is at least 6
Evaluate.
4. 4 C1
7. 14 C12
3. 6 C4
5. 7 C4
6. 8 C3
8. 10 C7
9. 9 C3
10. 100 C2
11. How many combinations can be formed from the letters in the word LIGHT, taking them:
a) 4 at a time?
b) 3 at a time?
c) 2 at a time?
12. How many combinations can be formed from the letters in the word TRIANGLE, taking them:
a) 7 at a time?
b) 5 at a time?
c) 2 at a time?
13. A club has 15 members; how many different combinations of 5 members can be chosen to sit
in the front row for the club picture?
14. A sample of 4 flashlights taken from a batch of 40 flashlights is to be inspected. How many
different samples could be selected?
15. How many line segments can be drawn by joining two points, given six points, no three of
which are collinear?
16. At the Hamburger Hut you can order hamburgers with cheese, onion, pickle, relish, mustard,
lettuce, or tomato. How many different combinations of the “extras” can you order, choosing
any three of them?
17. Seven points lie on a circle. How many inscribed triangles can be constructed having any
three of these points as vertices?
18. Students are required to answer any eight out of ten questions on a certain test. How many
different combinations of eight questions can a student choose to answer?
19. Ten points lie on the circumference of a circle. How many inscribed quadrilaterals can be
drawn having these points as vertices?
20. How many different 5-card hands can be dealt from a pack of 52 cards?
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Note: A standard (bridge) deck of cards consists of 4 suits (diamonds, clubs, hearts, and spades)
of 13 cards each. Within each suit, the Jack, Queen and King are called “face cards” and the
remaining cards are numbered 2 to 10 and Ace.
21. How many 13-card hands having exactly 10 spades can be dealt?
22. How many 13-card hands having exactly 11 cards from any suit can be dealt?
23. How many 5-card hands having exactly 1 spade, 2 hearts, and the other cards from the
remaining suits can be dealt?
24. How many 10-card hands having exactly 4 spades, 3 hearts, and 3 diamonds can be dealt?
25. In how many ways can 4 or more students be selected from 8 students?
26. In how many ways can 3 balls be drawn from a bag containing 4 green and 5 red balls if:
a) 2 must be green and 1 red?
b) all must be the same color?
n!
27. Prove that n Cr  n Cnr using n Cr 
r (n  r )!
28. Show that the total number of subsets of a set having n elements is 2 n . (Hint: Each member
of the set is or is not selected in forming a subset. Recall that the empty set is defined to be a
subset of every set.)
Practice Set E: Sample Spaces and Events (Page 733)
Two-dice Experiment
Suppose you roll tow dice, one red and one green. An outcome in this experiment can be
represented by the ordered pair ( r , g ) . In this pair, r is the number up on the red die and g is
the number turned up on the green die. The sample space for the two-dice experiment is shown
in this graph:
For exercises 1-5 refer to the Two-dice Experiment above.
1. How many different elements are there in the sample space?
2. Specify the event that both dice turn up the same number.
3. Specify the event that the numbers turned up on the two dice total ten.
4. Specify the event that the number turned up on the red die is one more than the number
turned up on the green die.
5. Specify the event that the sum of the numbers turned up on the two dice is greater than
seven.
6. Specify the sample space for tossing a penny, a dime, and a quarter. Specify the event that at
least two coins turn up tails.
7. A coin is tossed and a die is rolled. Specify the sample space. Specify the event that the
number turned up on the die is less than five.
8. Two bags contain marbles. The first bag contains one red marble and one white marble. The
second bag contains one red marble, one white marble, and one blue marble. One marble is
drawn from each bag. Specify the sample space. Specify the event that neither marble is red.
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For exercise 9-15, refer to the Two-dice Experiment above.
9. Specify the event that r  g  9 .
10. Specify the event that r  g .
11. Specify the event that r is a factor of g .
12. Specify the event that g  4 or r  3 .
13. Specify the event that r  g  3 or r  g  1
14. Specify the event that r  g is prime and g is a perfect square.
15. Specify the event that r is a multiple of 3 and r  g is a multiple of 2.
Practice Set F: Probability (Page 736)
1. One card is drawn at random from a 52-card bridge deck. Find the probability of each event.
a. It is a king.
b. It is a club.
c. It is the jack of hearts.
d. It is a red queen.
e. It is a 5 or a 6.
f. It is a red club.
2. A letter is drawn at random from those in SQUARE. Find the probability of each event.
a. It is a vowel
b. It is a consonant.
c. It comes from the first half of the alphabet.
3. One marble is drawn at random from a bag containing 2 white, 4 red, and 6 blue marbles. Find
the probability of each event.
a. It is blue.
b. It is black.
c. It is not white.
d. It is either red or white.
4. A box contains 20 slips of paper, numbered 1-20. A slip of paper is drawn from the box and the
number is noted. Find the probability of each event.
a. It is an 8.
b. It is an even number.
c. It is divisible by 3.
d. It is greater than 15.
e. It is less than 0.
f. It is a positive integer less than 21.
5. Three coins are tossed. Find the probability of each event.
a. All come up heads.
b. All come up tails.
c. Two come up tails and one comes up heads. d. At least one comes up tails.
6. At a class reunion, a television set is to be given as a door prize to the person whose ticket stub
is drawn at random from a bowl. A total of 190 tickets, numbered 1-190, are sold. Find the
probability that the winning number is:
a. 125.
b. between 79 and 179.
c. divisible by 10.
7. Of 1,000,000 income tax returns received by a tax collector, all are checked for arithmetic
accuracy and 9000 returns are checked thoroughly. For a given return, find the probability of
each event.
a. It is checked for arithmetic
b. It is checked thoroughly.
c. It is not checked thoroughly
accuracy.
8. Rebecca picked four kinds of apples: MacIntosh, Baldwin, Cortland, and Red Delicious. She
picked twice as many MacIntosh apples as Baldwin apples, and twice as many Baldwin apples as
Cortland or Red Delicious apples. If she chooses an apple at random from a basket containing all
the apples, what is the probability she chooses:
a. a MacIntosh apple? b. a Baldwin apple?
c. either a Cortland or a Red Delicious apple?
9. A bag contains 2 red, 4 yellow, and 6 blue marbles. Two marbles are drawn at random. Find
the probability of each event.
a. Both are red.
b. Both are yellow.
c. Both are blue.
d. Neither is blue
e. One is red and one is yellow.
10. Two cards are drawn at random from a 52-card bridge deck. Find the probability of each
event.
a. Both are spades.
b. Both are red.
c. Neither is a club.
d. Both are tens.
11. A bridge hand consists of 13 cards drawn at random from a 52-card bridge deck. Find the
probability of each event.
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a. A hand contains all four kings.
b. A hand contains no aces.
c. A hand contains no king, queen, or jack.
d. A hand contains all red cards.
Practice Set G: Mutually Exclusive and Independent Events (Page 744)
1. Two dice are rolled. What is the probability that both come up 4?
2. A single ball is drawn from a bag containing 4 red, 5 white, and 2 green balls. Find the
probability of each event.
a. A red or a green ball is drawn.
b. A white or a red ball is drawn.
3. There are 5 green, 2 white, and 3 red jerseys in a gym bag. A player picks a jersey at random,
puts it on, and then picks a second jersey for his teammate.
a. Find the probability that the first jersey is
b. Find the probability that the first jersey is
green and the second jersey is green. Are
white and the second jersey is red. Are these
these events independent?
events independent?
4. In a box, there are 3 red, 2 blue, and 3 yellow pastels. Doris randomly selects one, returns it,
and then selects another.
a. Find the probability that the first pastel is
b. Find the probability that the first pastel is
blue and the second pastel is blue. Are these
yellow and the second pastel is red. Are these
events independent?
events independent?
5. A die and a coin are tossed. Let A be the event that the die turns up odd and B the event that
the coin turns up heads.
a. Specify the sample space for the experiment. b. Specify the simple events in A, B, A  B, and
A B .
c. Find the probability of A, B, A  B, and
d. Are A and B mutually exclusive? Are they
independent?
A B .
6. A red and a green die are rolled. Let A be the event that the red die turns up 3 and B the event
that the sum of the numbers is 8.
a. Find the probability of A, B, A  B, and
b. Are A and B independent events?
A B .
7. Two dice are rolled. Find the probability of each event.
a. The sum of the numbers up is 9.
b. Either the sum of the numbers up is 6 or
both numbers up are 4.
8. Two cards are drawn from a 52-card bridge deck. Find the probability of each event.
a. Both are tens.
b. Both are aces.
c. Either both are tens or both are aces.
9. A coin is tossed three times. Find the probability of each event, then tell whether the events
are independent.
a. At least two tosses come up tails
b. At least one toss comes up heads.
10. A card is drawn from a 52-card bridge deck, replaced, the deck shuffled, and a second card is
drawn. Find the probability of each event.
a. Both cards are sevens.
b. Both cards are red.
11. If a set of six books is placed randomly on a shelf, what is the probability that they will be
arranged in either correct or reverse order?
12. Eleven people attend a conference. Four are executives, six are engineers, and one is a
lawyer. Three executives, two engineers, and the lawyer are women. A telegram arrives for one
of the eleven people. Find the probability of each event. Then tell whether the events are
independent.
a. The telegram is for an executive.
b. The telegram is for a woman.
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13. A card is drawn from a 52-card bridge deck. Let A be the event that the card is red, B the
event that is a 2, and C the event that it is either an 8 or a 9. Which of the following are
independent events?
a. A and B
b. A and C
c. B and C
14. When Carlos shoots a basketball, the probability that he will make a basket is 0.4. When Brad
shoots, the probability of a basket is 0.6. What is the probability that at least one basket is made
if Carlos and Brad take one shot each?
15. The probability that Leon will ask Frank to be his tennis partner is ¼ , that Paula will ask Frank
is 1 3 , and that Ray will ask Frank is 3 4 . Find the probability of each event.
a. Paula and Leon ask him.
b. Ray and Paula ask him, but Leon does not.
c. At least two of the three ask him.
d. At least one of the three asks him.
16. According to the weather reports, the probability of rain on a certain day is 70% in Yellow
Falls and 50% in Copper Creek. Find the probability of each of the following events.
a. It will rain in Yellow Falls, but not in Copper
b. It will rain in both cities.
Creek.
c. It will rain in neither city.
d. It will rain in at least one of the cities.
17. Two cards are drawn from a 52-card bridge deck. Find the probability of each event.
a. Both are red.
b. Both are queens.
c. At least one is black or not a queen.
Practice Set K: Permutations and Combinations (pg. 580 Brown)
3. Ten students each submit a woodworking project in an industrial arts competition. There are
to be first-, second-, and third-place prizes plus an honorable mention. In how many ways can
these awards be made?
4. A teacher has a collection of 20 true-false questions and wishes to chooses 5 of them for a
quiz. How many quizzes can be made if the order of the questions is considered (a) important?
(b) unimportant?
5. Each of the 200 students attending a school dance has a ticket with a number for a door prize.
If 3 different numbers are selected, how many ways are there to award the prizes, given that the
3 prizes are (a) identical? (b) different?
6. Suppose you bought 4 books and gave one to each of 4 friends. In how many ways can the
books be given if they are (a) all different? (b) all identical?
7. Eight people apply for 3 job positions. In how many different ways can the 3 positions be
filled if the positions are (a) all different? (b) all the same?
10. Of the 12 players on a school’s basketball team, the coach must choose 5 players to be in the
starting lineup. In how many ways can this be done if the playing positions are (a) considered?
(b) not considered?
11a. A hiker would like to invite 7 friends to go on a trip but has room for only 4 of them. In how
many ways can they be chosen?
11b. If there were room for only 3 friends, in how many ways could they be chosen? How is
your answer related to the answer for part (a)? Why?
17.A certain chain of ice cream stores sells 28 different flavors, and a customer can order a
single-, double-, or triple-scoop cone. Suppose that the order of flavors is important and that the
flavors can be repeated. How many possible cones are there?
18. Refer to Exercise 17 and find the number of double-scoop ice cream cones that are possible
if repetition of flavors is allowed but the order of flavors is unimportant.
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19. Three couples go to the movies and sit together in a row of six seats. In how many ways can
these people arrange themselves if each couple sits together?
20. A mathematics teacher uses 4 algebra books, 2 geometry books, and 3 precalculus books for
reference. In how many ways can the teacher arrange the books on a shelf if books covering the
same subject matter are kept together?
21. From a standard deck of 52 cards, 5 cards are dealt and the order of the cards is
unimportant. In how many ways can you receive (a) all face cards? (b) no face cards? (c) at least
one face card?
22. Answer part (c) of Exercise 21 if the order of receiving the 5 cards is important?
25. Solve for n: n C2  45
Practice Set L: Chapter Review (pg. 760)
1. How many positive integers less than 45 can be formed by using the digits 1, 2, and 3?
2. In how many ways can 4 cards be selected, one after the other, from a deck of 10 cards, if
selected cards are not returned to the deck?
3. In how many ways can 6 books, taken 3 at a time, be arranged on a shelf?
4. How many different permutations can be made using all the letters in the word ADDRESS?
5. In how many ways can 4 players be chosen from 9 players?
6. Three coins are tossed. Specify the sample space.
7. Three coins are tossed. What is the probability that at least two heads turn up?
8. A dime and a nickel are tossed. Let A be the event that the dime turns up heads and B the
event that the nickel turns up tails. What is the probability of A B ?
9. If A and B are mutually exclusive events, which of the following relationships applies?
a. P  A B   P  A  P  B 
b. P  A B   0
c. P  A B   P  A  P  B 
d. P  A B   P  A  P  B 
Practice Set M: Mixed Combinatorics (Brown pg. 587)
1. Three identical door prizes are to be given to three lucky people in a crowd of 100. In how
many ways can this be done?
2. The license plates in a certain state consist of 3 letters followed by 3 nonzero digits. How
many such license plates are possible?
3. How many 4-digit numbers (a) contain no 0’s (b) begin with an even digit and end with an odd
digit?
4. A student must take four final exams, scheduled by a computer, during the morning and
afternoon testing periods on Monday through Friday of exam week. If the order of the student’s
four exams is important, in how many ways can a computer schedule the exams?
5. A railway has 30 stations. On each ticket, the departure station and the destination station
are printed. How many different tickets are possible?
6. In how many ways can the letters of each of the following words be arranged?
a. RADISH
b. SQUASH
c. TOMATO
7. There are 3 roads from town A to town B, 5 roads from town B to town C, and 4 roads from
town C to town D. How many ways are there to go from A to D via B and C? How many different
round trips are possible?
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8. A teacher must pick 3 high school students from a class of 30 to prepare and serve food at the
junior high school picnic. How many choices are possible?
13. A town council consists of 8 members including the mayor.
a. How many different committees of 4 can be chosen from this council?
b. How many of these committees include the mayor?
c. How many do not include the mayor?
ANSWERS
Practice Set A
1. 240
2. 1024
3. 59,049
5. 30
6. 260,000
7. 2401
9. 75
10. 93
11. 10
13. 300
14. 37,856
15. 12
17. 11664 min (  8 days) 18. 65,536
19. 160,000
Practice Set B
1. 15
2. 144
3. 24
5. 20
6. 3,628,800
7. 120
9. 120
10. 24
11. 720
13. 180
14. 85
21. 18
Practice Set C
1. 1260
2. 30
3. 34,650
5. 630
6. 50,400
7. 30
9. 210
10. 1260
11. 60
13. 10
14. 2520
Practice Set D
1a. , K , L , M  , K , L , K , M  , L, M  , K , L, M 
4. 15,600
8. 20
12. 125
16. 11
20. 8315
4. 6840
8. 30
12. 120
22. 19
4. 20
8. 20
12. 30
1b. K , L , K , M  , L, M  , K , L, M 
2a. 2, 4 , 2,6 , 2,8 , 4,6 , 4,8 , 6,8
2b. 6 , 8 , 2, 4 , 2,6 , 2,8 , 4,6 , 4,8 , 6,8, 2, 4,6, 2, 4,8, 2,6,8 , 4,6,8 , 2, 4,6,8
3. 15
7. 91
11a. 5
12b. 56
15. 15
19. 210
23. 329,550
26b. 14
Practice Set E
1. 36
4. 4
8. 120
11b. 10
12c. 28
16. 35
20. 2,598,960
24. 58,484,140
5. 35
9. 84
11c. 10
13. 3003
17. 35
21. 2,613,754
25. 163
6. 56
10. 4950
12a. 8
14. 91,390
18. 45
22. 231,192
26a. 30
1,1 ,  2, 2 , 3,3 ,  4, 4 , 5,5 , 6,6
4.  2,1 ,  3, 2 ,  4,3 , 5, 4  ,  6,5 
2.
 4,6 , 5,5 , 6, 4
5.  2,6 ,  3,5 , 3,6 ,  4, 4  ,  4,5 ,  4,6  , 5,3 , 5, 4  , 5,5  , 5,6  ,  6, 2 ,  6,3 ,  6, 4 ,  6,5 ,  6,6
3.
874005280 Page 9
6.
 H , H , H  ,  H , H , T  ,  H , T , H  , T , H , H  ,  H , T , T  , T , H , T  , T , T , H  , T , T , T ;
 H , T , T  , T , H , T  , T , T , H  , T , T , T 
 H ,1 ,  H , 2  ,  H ,3 ,  H , 4  ,  H ,5 ,  H , 6  , T ,1 , T , 2  , T ,3 , T , 4  , T ,5  , T , 6 ;
 H ,1 ,  H , 2  ,  H ,3 ,  H , 4  , T ,1 , T , 2  , T ,3 , T , 4 
8.  R, R  ,  R,W  ,  R, B  , W , R  , W ,W  , W , B ;W ,W  , W , B 
9.  3,6 ,  4,5 , 5, 4  ,  6,3
10.  2,1 ,  3,1 , 3, 2 ,  4,1 ,  4, 2 ,  4,3 , 5,1 , 5, 2  , 5,3 , 5, 4  ,  6,1 ,  6, 2 ,  6,3 ,  6, 4 ,  6,5
11. 1,1 , 1, 2 , 1,3 , 1, 4 , 1,5 , 1,6 ,  2, 2  ,  2, 4  ,  2,6  , 3,3 ,  3,6 ,  4, 4 , 5,5 ,  6,6 
7.

1,1 , 1, 2  , 1,3 , 1, 4  , 1,5  , 1, 6  ,  2,1 ,  2, 2  ,  2,3  ,  2, 4  ,  2,5 ,  2, 6  , 

12. 


 3,1 ,  3, 2  ,  3,3 ,  3, 4  ,  3,5  ,  3, 6  ,  4,5  , 5,5  ,  6,5  ,  4, 6  ,  5, 6  ,  6, 6  

13. 1, 2 ,  2,1 , 3, 2 ,  4,3 , 5, 4  ,  6,5
14. 1,1 ,  2,1 ,  4,1 ,  6,1 , 1, 4  , 3, 4 
15.  3,1 ,  3,3 ,  3,5 ,  6, 2  ,  6, 4  ,  6,6 
Practice Set F
1a. 131
1e.
2
13
1b. 14
1f. 0
2c.
1
3
3a.
3d.
1
2
3
10
1
4
4b. 12
4f. 1
4c.
4d.
4a. 201
4e. 0
5a.
1
8
5b.
1
8
5c.
3
8
5d.
7
8
6a.
1
190
6b.
99
190
6c.
1
10
7a. 1
7b.
9
1000
7c.
991
1000
8a.
1
2
8b.
1
4
8c.
1
4
9a.
1
66
9b.
1
11
9c.
5
22
9d.
5
22
9e.
4
33
10a.
1
17
10b.
25
102
10c.
19
34
11a.
11
4165
11b.
6327
20,825
11c.
1,263,994
66,703,105
10d.
1
221
11d.
19
1,160,054
1c.
1
2
Practice Set G
1. 361
2a.
6
11
3b.
4a.
1
16
1
15
; no
; yes
1
52
1d.
1
26
2a. 12
3b. 0
2b.
1
2
3c.
5
6
2b.
9
11
4b.
9
64
3a. 92 ; no
; yes
5a. 1, H  ,  2, H  ,  3, H  ,  4, H  ,  5, H  ,  6, H  , 1, T  ,  2, T  , 3, T  ,  4, T  , 5, T  ,  6, T 
A  1, H  ,  3, H  ,  5, H  , 1, T  ,  3, T  ,  5, T  ;
5b.
B  1, H  ,  2, H  ,  3, H  ,  4, H  ,  5, H  ,  6, H  ;
A  B  1, H  ,  2, H  ,  3, H  ,  4, H  ,  5, H  ,  6, H  , 1, T  ,  3, T  ,  5, T  ;
A  B  1, H  ,  3, H  ,  5, H 
6b. no
874005280 Page 10
5c. 12 ; 12 ; 43 ; 14
5d. no; yes
6a. 16 ; 365 ; 185 ; 361
7a.
7b.
8a.
1
9
1
6
1
221
8b.
1
221
10a.
1
169
8c.
2
221
10b.
Practice Set K
3. 5040
5b. 7,880,400
11b. 35
20. 1728
22. 232914240
Practice Set L
1. 12
5. 126
8. ¼
Practice Set M
1. 161700
4. 5040
6c. 180
13b. 35
874005280 Page 11
9b. 78 ; not independent
1
2
1
11. 360
13b. yes
12a. 114
13c. no
16a. 35%
15b. 163
16b. 35%
15c. 19
48
16c. 15%
17a.
17b.
17c.
1
4
13a. yes
12b. 116 ; not independent
14. 0.76
15a. 121
15d. 78
16d. 85%
9a.
25
102
4a. 1,860,480
10a. 95040
17. 22764
21a. 792
25. 10
1
221
4b. 15,504
10b. 792
18. 406
21b. 658008
1325
1326
5a. 1,313,400
11a. 35
19. 48
21c. 1940952
2. 5040
3. 120
6. HHH, HHT, HTH, HTT, THH, THT, TTH, TTT
9. C
4. 1260
7. ½
2. 12812904
5. 870
7. 60; 3600
13c. 35
3b. 2000
6b. 360
13a. 70
3a. 6561
6a. 720
8. 4060