Combinations, Permutations, and Related Counting Problems
Note: The number of permutations of n things taken r at a time = P(n, r).
The number of combinations of n things taken r at a time = C(n, r).
Connect each problem number to both the a and b answers.
1. a) C(9, 3) =
b) How many distinct 5-letter permutations are there for the letters of the word
ACORN, using all of the letters each time?
2. a) C(8, 2) =
b) How many distinct 6-letter permutations are there for the letters of the word
ADIDAS, using all of the letters each time?
3. a) C(7, 4) =
b) How many arrangements are there for 7 people seated at a circular table with 7
seats?
4. a) P(5, 3) =
b) How many ways may 8 keys be arranged on a key ring?
5. a) P(5, 2) =
b) How many different 5-digit license plates may be made if the first digit cannot be
zero and repetitions of the digits are allowed?
6. a) P(7, 3) =
b) How many different ways can you answer a 6-question True-false exam?
7. a) C(9, 6) =
b) How many different ways can you answer a 7-question multiple choice exam
(with 3 choices) if you know that no two consecutive answers are the same?
8. a) How many different 5-card hands may be dealt from a standard deck of 52 cards?
Express the answer as a permutation or combination - do not compute.
b) C(9, 6) =
9. a) C(7, 3) =
b) How many different Bridge hands (13 cards) may be dealt from a standard deck
of 52 cards? Express the answer as a permutation or combination - do not compute.
10. a) How many 3-letter initials may be made from ACMLO, if repetition of the letters is
allowed?
b) How many different committees consisting of 3 males and 2 females may be formed
from 36 males and 25 females? Express the answer as
a permutation or combination - do not compute.
11. a) Suppose a sundae consists of 1 flavor of ice cream; 1 sauce topping; marshmallow
or whipped cream; and either a nut or a cherry. If 31 flavors are available, and 7
toppings are available, how many different sundaes are possible?
b) How many 2-digit numbers may be written using 2, 3, 4, 5, 6 if repetition
of the digits is not allowed?
12. a) A statistician must choose a sample of 3 people from a group of 52 people. How
many different samples are possible?
b) How many 3-letter sorority names can be formed from the Greek letters,
if repetition of the letters is not allowed?
13. Complete the design without further clues.
