Download WS Chapter 11

WS Chapter 11
Discrete Math
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1. A restaurant offers 11 entrees and 10 desserts. In how many ways can a person order a
two-course meal?
2. A restaurant offers a choice of 5 salads, 6 main courses, and 3 desserts. How many
possible 3-course meals are there?
3. You are taking a multiple-choice test that has 8 questions. Each of the questions has 3
choices, with one correct choice per question. If you select one of these options per question
and leave nothing blank, in how many ways can you answer the questions?
4. License plates in a particular state display 2 letters followed by 3 numbers. How many
different license plates can be manufactured?
5. A person can order a new car with a choice of 10 possible colors, with or without air
conditioning, with or without heated seats, with or without anti-lock brakes, with or without power
windows, and with or without a CD player. In how many different ways can a new car be
ordered in terms of these options?
6. There are 4 performers who are to present their acts at a variety show. How many different
ways are there to schedule their appearances?
7. A teacher and 8 students are to be seated along a bench in the bleachers at a basketball
game. In how many ways can this be done if the teacher must be seated in the middle and a
difficult student must sit to the teacher's immediate left?
8. A club elects a president, vice-president, and secretary-treasurer. How many sets of officers
are possible if there are 11 members and any member can be elected to each position? No
person can hold more than one office.
9. In a contest in which 7 contestants are entered, in how many ways can the 4 distinct prizes
be awarded?
10. In how many distinct ways can the letters in ACCOUNTING be arranged?
11. A signal can be formed by running different colored flags up a pole, one above the other.
Find the number of different signals consisting of 8 flags that can be made if 4 of the flags are
white, 3 are red and 1 is blue.
For problems 12 and 13, does the following problem involve permutations or
combinations?
12. One hundred people purchase lottery tickets. Three winning tickets will be selected at
random. If first prize is $100, second prize is $50, and third prize is $25, in how many different
ways can the prize be awarded?
13. Five of a sample of 100 computers will be selected and tested. How many ways are there
to make this selection?
14. From 10 names on a ballot, a committee of 3 will be elected to attend a political national
convention. How many different committees are possible?
15. In how many ways can a committee of three men and four women be formed from a group
of 12 men and 12 women?
16. To win at LOTTO in a certain state, one must correctly select 6 numbers from a collection of
51 numbers (one through 51). The order in which the selections are made does not matter.
How many different selections are possible?
17. You are dealt one card from a standard 52-card deck. Find the probability of being dealt a
picture (face) card.
18. You are dealt one card from a standard 52-card deck. Find the probability of being dealt an
ace or a 8.
19. A fair coin is tossed two times in succession. The set of equally likely outcomes is {HH, HT,
TH, TT}. Find the probability of getting the same outcome on each toss.
20. A single die is rolled twice. Find the probability of getting two numbers whose sum is less
than 13.
21. A single die is rolled twice. Find the probability of getting two numbers whose sum is
greater than 9.
22. This problem deals with eye color, an inherited trait. For purposes of this problem, assume
that only two eye colors are possible, brown and blue. We use b to represent a blue eye gene
and B a brown eye gene. If any B genes are present, the person will have brown eyes. The
table shows the four possibilities for the children of two Bb (brown-eyed) parents, where each
parent has one of each eye color gene. Find the probability that these parents give birth to a
child who has blue eyes.
Second Parent
B
b
First
B
BB
Bb
Parent
b
Bb
bb
23. In 1999 the stock market took big swings up and down. A survey of 956 adult investors
asked how often they tracked their portfolio. The table shows the investor responses. What is
the probability that an adult investor tracks his or her portfolio daily?
How Frequently?
Response
Daily
226
Weekly
262
Monthly
284
Couple times a year 130
Don't track
54
Use the following chart for 24 and 25. The chart below shows the percentage of people in
a questionnaire who bought or leased the listed car models and were very satisfied with
the experience.
Model A
Model B
Model C
Model D
Model E
Model F
81%
79%
73%
61%
59%
57%
24. With which model was the greatest percentage satisfied? Estimate the empirical probability
that a person with this model is very satisfied with the experience. Express the answer as a
fraction with a denominator of 100.
25. The empirical probability that a person with a model shown is very satisfied with the
experience is 57/100. What is the model?
26. Amy, Jean, Keith, Tom, Susan, and Dave have all been invited to a birthday party. They
arrive randomly and each person arrives at a different time. In how many ways can they arrive?
In how many ways can Jean arrive first and Keith last? Find the probability that Jean will arrive
first and Keith will arrive last.
27. Six students A, B, C, D, E, F are to give speeches to the class. The order of speaking is
determined by random selection. Find the probability that… (a) E will speak first. (b) C will
speak fifth and B will speak last. (c) the students will speak in the following order: DECABF. (d)
A or B will speak first.
28. A group consists of 6 men and 5 women. Four people are selected to attend a conference.
In how many ways 4 people be selected from this group of 11? In how many ways can 4 men
be selected from the 6 men? Find the probability that the selected group with consist of all men.
29. A box contains 28 widgets, 4 of which are defective. If 4 are sold at random, find the
probability that… (a) all are defective (b) none are defective.
30. If you are dealt 6 cards from a shuffled deck of 52 cards, find the probability of getting 3
jacks and 3 aces.
WS Chapter 11 Answers
1. 110
2. 90
3. 6561
4. 676,000
5. 320
6. 24
7. 5040
8. 990
9. 840
10. 907,200
11. 280
12. Permutations
13. Combinations
14. 120
15. 108,900
16. 18,009,460
17. 3/13
18. 2/13
19. 1/2
20. 1
21. 1/6
22. 1/4
23. 226/956; 0.236
24. Model A; 81/100
25. F
26. 720; 24; 1/30
27. 1/6; 1/24; 1/720; 1/3
28. 330, 15, 1/22
29. 1/20475; 506/975
30. 2/2544825