Deck 9: Discrete Mathematics

Question 1

Tell whether permutations or combinations are being described.
4 cards are selected from a deck of 52 to form a hand for a certain card game.

A) Permutations
B) Combinations

Answer 1

B

Question 2

How many automobile license plates can be made involving 4 letters followed by 2 digits?

A) 45,697,600
B) 457,076
C) 45,718,100
D) 45,687,344

Answer 2

A

Question 3

Evaluate.
8!

A) 5040
B) 20,160
C) 80,640
D) 40,320

Answer 3

D

Question 4

Tell whether permutations or combinations are being described.
14 students are selected to form a committee.

A) Combinations
B) Permutations

Question 5

How many automobile license plates can be made involving 2 letters followed by either 3 or 4 digits?

A) 7,536,000
B) 7,416,000
C) 7,436,000
D) 7,476,000

Question 6

The code for some garage door openers consists of 15 electrical switches that can be set to "+" , "0" , or "-" by the owner. With this type of opener, how many different codes are possible?

A) 14,350,167
B) 14,347,707
C) 14,348,907
D) 14,348,659

Question 7

Evaluate.
4P3

A) 4
B) 2
C) 12
D) 24

Question 8

Evaluate.

Question 9

Tell whether permutations or combinations are being described.
7 digits are selected (with possible repetition) to form a code for an alarm system.

A) Combinations
B) Permutations

Question 10

In how many ways can you answer the questions on an exam that consists of 6 multiple choice questions, each of which has 3 answer choices?

A) 1569
B) 499
C) 216
D) 729

Question 11

In how many ways can you answer the questions on an exam that consists of 8 multiple choice questions, each of which has 4 answer choices, followed by 5 true-false questions?

A) 2,097,152
B) 2,221,982
C) 2,084,702
D) 2,680,257

Question 12

Tell whether permutations or combinations are being described.
4 musicians are selected to form a band.

A) Permutations
B) Combinations

Question 13

How many 5 letter strings can be formed with the letters D , E , F , and G , if each letter can be used more than once?

A) 1024
B) 1104
C) 1224
D) 984

Question 14

Tell whether permutations or combinations are being described.
10 pageant contestants are selected to be given awards and titles, the first being the winner, the second being the first runner-up, the third being the second runner-up, and so forth.

A) Permutations
B) Combinations

Question 15

A person ordering a certain model of car can choose any of 9 colors, either manual or automatic transmission, and any of 4 audio systems. How many ways are there to order this model of car?

A) 68
B) 82
C) 80
D) 72

Question 16

In the "Big Bucks" lottery game, a person is to pick 5 digits from 0 to 9 in correct order. If a number can be repeated, how many ways are there to play the game?

A) 9,765,625
B) 1,000,000
C) 100,000
D) 1,953,125

Question 17

How many automobile license plates can be made involving 3 letters followed by 4 digits, if letters cannot be repeated ( used more than once ) but digits can be repeated ?

A) 155,971,400
B) 175,760,000
C) 156,000,000
D) 156,269,020

Question 18

Tell whether permutations or combinations are being described.
4 dishwashers are ranked for performance by an independent laboratory.

A) Permutations
B) Combinations

Question 19

In how many ways can you answer the questions on an exam that consists of 20 true-false questions?

A) 1,048,656
B) 1,048,576
C) 1,048,696
D) 1,048,512

Question 20

Evaluate.

Question 21

Solve.
How many different three-digit numbers can be written using digits from the set {5, 6, 7, 8, 9} without any repeating digits?

A) 20
B) 60
C) 10
D) 120

Question 22

Solve.
There are 6 women running in a race. How many first, second, and third place possibilities can occur?

A) 20
B) 18
C) 120
D) 216

Question 23

Solve.
A signal is made by placing 3 flags, one above the other, on a flag pole. If there are 9 different flags available, how many possible signals can be flown?

A) 84
B) 504
C) 27
D) 729

Question 24

Solve the problem.
How many committees of 5 people can be selected from 9 men and 8 women if the committee must have 3 men and 2 women?

A) 2492
B) 2352
C) 2332
D) 28,224

Question 25

Expand the binomial.

Question 26

Solve the problem.
There are 14 people in a club. A committee of 6 persons is to be chosen to represent the club at a conference. In how many ways can the committee be chosen?

A) 360,360
B) 2,162,160
C) 3003
D) 3429

Question 27

Solve the problem.
A game involves choosing 8 numbers from the numbers 1 through 13. In how many ways can this be done?

A) 1287
B) 1267
C) 51,891,840
D) 1295

Question 28

Solve.
A musician plans to perform 5 selections for a concert. If he can choose from 7 different selections, how many ways can he arrange his program?

A) 21
B) 35
C) 2520
D) 16,807

Question 29

Solve the problem.
There are 11 essay questions on a test. Students must select 3 questions to write essays on. In how many ways can the 3 questions be chosen?

A) 990
B) 172
C) 165
D) 163

Question 30

Solve.
In how many ways can the letters in the word PAYMENT be arranged if the letters are taken 6 at a time?

A) 42
B) 5040
C) 7
D) 2520

Question 31

Solve.
How many ways can a president, vice-president, and secretary be chosen from a club with 9 members?

A) 6
B) 504
C) 84
D) 27

Question 32

Expand the binomial.

Question 33

Solve.
A baseball manager has 12 players of the same ability. How many 9 player starting lineups can he create?

A) 108
B) 79,833,600
C) 362,880
D) 220

Question 34

Expand the binomial.

Question 35

Solve.
In how many ways can 7 people line up for play tickets?

A) 5040
B) 1
C) 823,543
D) 7

Question 36

Solve.
How many different three-number "combinations" are possible on a combination lock having 28 numbers on its dial?

A) 19,656
B) 37,800
C) 18,900
D) 9828

Question 37

Solve the problem.
There are 10 different books on a table. In how many ways can 8 books be chosen?

A) 471
B) 226,800
C) 45
D) 1,814,400

Question 38

Solve the problem.
There are 12 books on a reading list for English I. Students must select 4 books to read from this list. In how many ways can the 4 books be selected?

A) 485
B) 515
C) 495
D) 11,880

Question 39

Solve the problem.
How many ways are there to choose 9 books from a collection of 12 different books?

A) 79,833,600
B) 55
C) 220
D) 660

Question 40

Solve the problem.
Cal is packing his suitcase to go on a trip. He wants to pack 4 pairs of pants chosen from the 6 pairs of pants in his closet and 3 shirts chosen from the 10 shirts in his closet. In how many ways can this be done?

A) 1800
B) 259,200
C) 43,200
D) 10,800

Question 41

Find the coefficient of the given term in the binomial expansion.

Question 42

Evaluate.

Question 43

Expand the binomial.

Question 44

Expand the binomial.

Question 45

Expand the binomial.

Question 46

Evaluate.

Question 47

Evaluate.

Question 48

Evaluate.

Question 49

Find the coefficient of the given term in the binomial expansion.

Question 50

Expand the binomial.

Question 51

Find the coefficient of the given term in the binomial expansion.

Question 52

Evaluate.

Question 53

Find the coefficient of the given term in the binomial expansion.

Question 54

Evaluate.

Question 55

Expand the binomial.

Question 56

Expand the binomial.

Question 57

Find the coefficient of the given term in the binomial expansion.

Question 58

Find the coefficient of the given term in the binomial expansion.

Question 59

Find the coefficient of the given term in the binomial expansion.

Question 60

Find the coefficient of the given term in the binomial expansion.

Question 61

Write out the first five terms of the sequence.

Question 62

Write out the first five terms of the sequence.

Question 63

Find the first six terms of the sequence.

Question 64

Find the first six terms of the sequence.

Question 65

Determine whether the sequence converges or diverges. If it converges, give the limit.

Question 66

Find the first six terms of the sequence.

Question 67

Determine whether the sequence converges or diverges. If it converges, give the limit.

Question 68

Determine whether the sequence converges or diverges. If it converges, give the limit.

Question 69

Find the first six terms of the sequence.

Question 70

Determine whether the sequence converges or diverges. If it converges, give the limit.

Question 71

Write out the first five terms of the sequence.

Question 72

Find an explicit rule for the nth term of the arithmetic sequence.

Question 73

Determine whether the sequence converges or diverges. If it converges, give the limit.

Question 74

Find an explicit rule for the nth term of the arithmetic sequence.

Question 75

Find an explicit rule for the nth term of the arithmetic sequence.

Question 76

Write out the first five terms of the sequence.

Question 77

Find the first six terms of the sequence.

Question 78

Find an explicit rule for the nth term of the arithmetic sequence.

Question 79

Find an explicit rule for the nth term of the arithmetic sequence.

Question 80

Write out the first five terms of the sequence.