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Combinatorics

Total questions: 14

Worksheet time: 22mins

Name
Class
Date
1.

Permutation or Combination: The student body of 30 students wants to elect a president, vice president, secretary, and treasurer.

a)

permutation

b)

combination

2.

Permutation or Combination: A group of 40 people are going to run a race. The top three runners earn gold, silver, and bronze medals.

a)

permutation

b)

combination

3.
How would you solve?
A book club offers a choice of 8 books from a list of 40.  In how many ways can a member make a collection?
a)
Permutation
b)
Combination
c)
Factorial
d)
MPC
4.
How would you solve?
From the 20 DVD's you purchased this past year, you plan to take five with you on vacation.  How many different sets of five DVD's can you take?
a)
Permutation
b)
Combination
c)
Factorial
d)
MPC
5.

Permutation or Combination: A group of 14 people need to take an elevator to the top floor. They will go in groups of seven. They are deciding who will take the elevator on its second trip.

a)

permutation

b)

combination

6.

solve the following combination: Amanda and Jimmy are planning trips to four countries this year. There are 8 countries they would like to visit. They are deciding which countries to skip.

a)

70

b)

45

c)

280

d)

260

7.

solve the following permutation: The student body of 40 students wants to elect a president, vice president, secretary, and treasurer.

a)

2479595

b)

2140140

c)

2193360

d)

4386720

8.

solve the following combination: Selecting which seven players will be in the batting order on a 9 person team.

a)

36

b)

30

c)

72

d)

18

9.
An election ballot asks voters to select three city commissioners from a group of six candidates.  In how many ways can this be done?
a)
6!
b)
120
c)
20
d)
3!
10.
The ski club with ten members is to choose three officers for captain, co-captain and secretary.  How many ways can those offices be filled?
a)
720
b)
120
c)
10!
11.
Eva has eight glasses of water.  In how many different orders can the glasses of water be arranged?
a)
8
b)
64
c)
8!
d)
56
12.
Rylan’s basketball team has 11 players. How many ways can his coach choose five starting players?
a)
462
b)
55440
c)
55
d)
1000
13.
Ashlyn needs to bring a dessert to her dinner party. If the bakery has eight pies to choose from, how many ways can Ashlyn choose three?
a)
336
b)
56
c)
24
d)
100
14.
In the orchestra, there are eight violinists in the front row. How many different ways can they be seated?
a)
40320
b)
1
c)
64
d)
8