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Sets and Combinations
1. For
S = the set of whole numbers
A = the set of numbers which are perfect squares
B = the set of positive even numbers
Describe the following
a. A’
b. A  B
c. A  B
d. A’  B’
e. (A  B)’
2. Find the indicated value for the given sets
S = {red, green, white, blue, gold}
D = {red, green}
E = {blue, white, gold}
Describe the following
a. n(S) b. n(D)
c. n(E’)
d. n(D  E) e. n(D  E)
3. If Z is a subset of X, but X is not a subset of Y, is it possible that Y
and Z are disjoint? IS this the only possibility? Illustrate your
answers with examples in the form of Venn diagrams.
4. a. for any set A, A   = A. Why?
b. for any set A, A   =  . Why?
c. give a simpler expression for A  A’ and A  A’.
5. Which is larger –
a. the number of arrangements of five out of nine objects or the
number of 5-subsets of a set with nine elements?
b. The number of ways of choosing 3 books from a shelf holding eight
different books or the number of possible lists of the first,
second, and third most popular books on that shelf? Why?
6. A club has 25 members –
a. In how many ways can a committee of three member be chosen?
b. In how many ways can the offices of president, secretary and
treasurer be filled?
7. Evaluate:
9
a.  
9
 
9
b.  
0
 
8. The school rock climbing team consists of 5 boys and 5 girls. How
many groups of 4 can be formed with –
a. no restrictions?
b. 4 boys?
c. 3 boys and 1 girl?
d. 2 boys and 2 girls
e. a boy and 3 girls f. four girls?
9. How many poker hands (five cards) are there with 3 aces and 2 kings?
10. Solve each equation for n, where n ε N.
 n 
 = 10
 n  2
a. 
n  1 
n
2
 n  2

 3 
b. 4   = 
 n  1
 =
 3 
c. 
n
 
2
n  n 
 =   + 

11. Prove that 
r  1  r   r  1
12. In how many ways can 22 members of the AP statistics class be selected toa. form a team of 3 for the upcoming math contest?
b. in how many of these cases would Ryan be a member?
c. in how many of these cases would Ryan not be a member?
13. a. How many different sums of money can be made from a $2-bill, a $5-bill
and a $10-bill?
b. How many different sums can be made if there were 5 $2-bills, 7 $5-bills
and 11 $10-bills?
14. A committee of students and teachers is being formed to study the issue of
student parking privileges. Fifteen staff members and eight students have
expressed interest in serving on the committee. In how many different ways
could a 5 person committee be formed that includes at least one teacher and
one student?
15. The prime factorization of 540 is 2 x 2 x 3 x 3 x 3 x 5. Find the number of
divisors of 540 other than 1.
16. In Paulina’s first year college program she must take 9 courses including at
least two science courses. If there are 5 science courses, 3 math courses, 4
language courses, and five business courses from which to choose, how many
different academic programs could she follow?
17. Five different signal flags are available to fly on a ship’s flagpole. How many
different signals can be sent using at least two flags?