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Permutations, Combinations and FCP

Total questions: 50

Worksheet time: 3hrs 34mins

Name
Class
Date
1.
Determine whether the following scenarios are a permutation or a combination:
 
Selecting a lead and an understudy for a school play.
a)
Combination
b)
Permutation
2.
In how many ways can 3 different vases be arranged on a tray?
 
a)
3
b)
9
c)
6
d)
12
3.
How many outfits are possible with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?
a)
15
b)
40
c)
80
d)
10
4.
How many 5-digit (numerical) passwords are possible for the school email system if the first digit cannot be 0?
a)
11,424,400
b)
10,967,424
c)
9000
d)
90,000
5.
There are 6 roads from Ponder to Justin, 2 roads from Justin to Halslet, and 3 roads from Haslet to Saginaw.  How many possible routes are there from Ponder to Saginaw using only these roads and no backtracking? 
a)
12
b)
11
c)
18
d)
36
6.
Homecoming has 7 candidates for King. How many ways can a King and a First Runner-up be chosen to form the Festival Court?
a)
23
b)
840
c)
42
d)
3,628,800
7.
Student council has 24 members.  In how many different ways can a president, vice-president, treasurer, historian, and secretary be selected?  
a)
5,100,480
b)
0
c)
42,504
d)
5.17 x 1021
8.
A team of 17 volleyball players needs to choose three players to refill the water cooler.  How many different ways can the players be chosen?  
a)
3360
b)
560
c)
4080
d)
680
9.
Find the possibilities when a group of 15 people are going to run a race.  The top 5 finishers advance to the finals.
a)
1.3 x 1012
b)
120
c)
3003
d)
360,360
10.
Picking a team of three people out of a group of 10.
a)
Permutation
b)
Combination
c)
Neither
11.
Choosing 3 toppings for your sundae out of a list of 15.
a)
Permutation
b)
Combination
c)
Neither
12.
Picking a President, Vice-President, and Secretary from a group of 12.
a)
Permutation
b)
Combination
c)
Neither
13.
How many ways can a president, vice president, and treasurer be elected from a group of 40 students?
a)
120
b)
59,280
c)
9,880
d)
2,354
14.
Ambry must submit 4 paintings as part of her
application to art school. If she has 25 to choose from, how many ways can she pick 4?
a)
12,650
b)
303,600
c)
100
d)
254
15.
How many outfits are possible with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?
a)
15
b)
40
c)
80
d)
10
16.
A disc jockey has to choose three songs for the last few minutes of his evening show.  If there are nine songs that he feels are appropriate for that time slot, then how many ways can he choose and arrange to play three of those nine songs?
a)
84
b)
504
c)
9!
d)
3!
17.
Robin has five different pairs of shoes that match with 6 different pairs of socks.  How many shoes-and-socks combinations can she make if she selects one pair of shoes and one pair of socks?
a)
1
b)
30
c)
5!
d)
6!
18.

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)

Fundamental Counting Principle (FCP)

19.

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)

Fundamental Counting Principle (FCP)

20.

How would you solve?

The model of car you are thinking of purchasing is available in nine different colors, three different styles and two sizes of motor. How many ways can you order the car?

a)

Permutation

b)

Combination

c)

Factorial

d)

Fundamental Counting Principle (FCP)

21.

How would you solve?

How many ways can you line up your eight trophies that you've won over the years on a shelf in your room?

a)

Permutation

b)

Combination

c)

Factorial

d)

Fundamental Counting Principle (FCP)

22.
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!
23.
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
24.
Sarah plays softball over the summer.  If there are 10 players on the team, how many ways can the coach make a batting order that includes all players?
a)
1
b)
3628800
c)
100
d)
1814400
25.
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
26.
A restaurant offers four appetizers, nine entrees,and three desserts. How many different ways can Angela choose a three course meal?
a)
36
b)
100
c)
108
d)
27
27.
Justin took a quiz with five multiple choice (A-D) and five true/false questions. How many different ways can he answer the questions?
a)
1024
b)
32
c)
32768
d)
25
28.
If Lucas owns 11 hoodies,how many ways can he choose four to bring on vacation?
a)
44
b)
7920
c)
330
d)
121
29.
Permutation, combination, or neither?
The batting order for seven players on a 12 person team.
a)
combination
b)
permutation
c)
neither
30.
Permutation, combination, or neither?
There are 45 applicants for three Computer Programmer job positions.
a)
combination
b)
permutation
c)
neither
31.
Permutation, combination, or neither?
A team of 8 basketball players need to choose a co-captain and captain.
a)
combination
b)
permutation
c)
neither
32.
What is the value of 8!
a)
40320
b)
36
c)
362880
d)
5040
33.
What is the formula for Permutations?
a)
n!
b)
n!∕(n-r)!
c)
n!∕(n-r)! r!
d)
r!∕(r-n)! n!
34.
What is the formula for Combinations?
a)
n!∕(n-r)! r!
b)
n!∕(n-r)!
c)
r!∕(r-n)! n!
d)
n!
35.

Simply the expression: 9P4

a)

36

b)

120

c)

35

d)

3024

36.

Simplify the expressions 6P5

a)

1

b)

30

c)

720

d)

6

37.

Simplify the expression 5C2

a)

20

b)

10

c)

120

d)

60

38.

Simplify the expression 9C6

a)

84

b)

54

c)

24

d)

124

39.

Simplify the expression 6!/2!

a)

12

b)

360

c)

30

d)

10

40.

Simplify the expression 7!/4!

a)

18

b)

260

c)

210

d)

24

41.
How many 2-digit numbers can you make using the digits 1, 2, 3, & 4 without repeating the digits?
a)
90
b)
100
c)
12
d)
24
42.
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
43.
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!
44.

Find the number of words, with or without meaning, that can be formed with the letters of the word ‘CHAIR’.

a)

5

b)

3125

c)

120

d)

25

45.

How many different arrangements can be made from COLLEGE?

a)

28

b)

720

c)

5040

d)

35280

46.

How many ways could you choose 2 different letters from SCHOOL?

a)

15

b)

120

c)

10

d)

360

47.

How many ways could you choose 2 different letters from PROBABILITY?

a)

3,628,800

b)

28

c)

55

d)

403,200

48.

How many ways can you choose a manager and assistant manager from a 9-person work team?

a)

81

b)

18

c)

72

49.

How many identification codes are possible by using 3 letters if no letter may be repeated?

a)

15,600

b)

75,350

c)

17,125

50.

Student council has 24 members. In how many different ways can a president, vice-president, treasurer, historian, and secretary be selected?

a)

5,100,480

b)

242,880

c)

42,504

d)

5,170,225

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