Combinations Worksheet With Answers Page 2
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4Example 2: The Canadian history class is preparing for its final examination. From a
class of 18 males and 12 females, how many study groups of 2 males and 3
females can be formed?
Order is not considered. There are two questions to be considered.
• How many ways can 2 males be chosen from 18?
• How many ways can 3 females be chosen from 12?
The answer is the product of these two combinations, C(18,2) and C(12, 3).
18
!
12
!
• C
=
•
C
(
18
,
) 2
(
12
) 3 ,
−
−
(
18
2
)!
! 2
(
12
3
)!
! 3
18
!
12
!
=
•
16
!
! 2
! 9
! 3
18
!
12
!
=
16
!
! 2
! 9
! 3
=
33
660
There are 33 660 possible combinations of 2 males and 3 females.
EXERCISES:
Note: Not all of these questions deal with combinations. Some are permutations!
1.
Describe the difference between a permutation and a combination.
2.
A starting baseball team is formed from a group of 12 players. Explain why this might be a
considered a permutation.
3.
A student approaches you and asks you for the permutation to your permutation lock. You
look at them with confusion and then say, “You mean what’s the combination to my
combination lock?” The student insists upon using the word permutation instead of the
word combination. Who is correct mathematically?
4.
Determine whether each situation involves a permutation or a combination.
a. 5 books on a shelf
b. a rummy hand of 7 cards
c. a seating chart in a classroom
d. 3-letter patterns, chosen from the letters in the word algebra
e. a hand of 5 cards from a deck of cards
f. a team of 5 people chosen from a group of 12 people
g. the answers on a true/false test
h. the batting order of the Los Angeles Dodgers
i. putting students in assigned sets
j. 8 guests seated around a table for dinner
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