Honors Discrete Practice Multiple Choice
CHAPTER 15: COUNTING, PROBABILITY, AND ODDS
Pick the MOST ACCURATE Answer Choice
For Questions #1 - 3: A license plate consists of any three capital letters (A to Z) followed by any five
numbers (0 to 9).
1) How many different license plates are possible?
A) 263 *105
B) 368
C) 265 * 103
D) 523 * 105
2) How many different license plates have no repeated characters?
A) 52*51*50*10*9*8*7*6
B) 62*61*60*59*58*57*56*55
C) 26*25*24*10*9*8*7*6
D) 26*25*24*23*105
3) How many different license plates start with an “A” and end with an odd number?
A) 1*51*50*9*8*7*6*5
B) 1*522*104*5
D) 1*262*104*5
C) 1*25*24*9*8*7*6*5
For Questions #4-7: A password consists of 9 characters. A character is any letter (A through Z) or digit
(0 through 9) which is case sensitive.
4) How many different passwords are possible?
A) 369
B) 529 + 109
C) 629
D) 529 * 109
5) How many different passwords do not contain a 4?
A) 619
B) 359
C) 529 + 99
D) 269 + 99
6) How many different passwords contain only letters?
A) 369
B) 529
C) 629
D) 269
7) How many different passwords contain exactly six 4’s and three B’s?
A) 6C4*3C2
B) 9C6*9C3
C) 9C6*3C3
D) 10C6*52C3
For # 8 - 9 : Four Seniors, Three Juniors, and Two Sophomores are waiting in line to pay their AP Fees at
the main office .
8) How many different ways could these students wait in line?
A) 24
B) 288
C) 387,420,489
D) 362,880
9) How many unique ways could these students wait in line if the sophomores were last two students in
line?
A) 10,080
B) 144
C) 9,565,938 D) 362,880
10) How many more ways can 10 juniors running for the positions of president, vice president, secretary,
and treasurer be selected when compared to 12 sophomores running for 5 identical positions of class
representative?
A) 94,830
B) 11,628
C) 4,320
D) 4,248
11) A starting line for a hockey team should consist of 3 offensive players, 2 defensive players, and 1
goaltender. A coach has 11 offensive players, 6 defensive players, and 2 goaltenders from which to
choose the starting line. How many unique starting lines can the coach create?
A) 132
B) 792
C) 4,950
D) 59,400
12) A starting line for a basketball team should consists of a center, power forward, small
forward, shooting guard, and point guard. The basketball team consists of 4 guards, 4
forwards, and 2 centers. How many unique starting lineups can begin a game?
A) 288
B) 792
C) 72
D) 30,240
For Questions # 13 - 15: Suppose a fair coin is flipped 6 times and it is
recorded whether the coin lands heads or tails.
13) What is the size of this sample space?
A) 720
B) 30
C) 15
D) 64
14) What is the probability of getting exactly 4 heads?
P4
A)
26
6
15)
C4
B)
26
6
P4
D)
26
1
C) 6
2
4
What is the probability of getting at least 4 tails?
C4 6 C5 6 C6
A)
26
24  25  26
C)
26
6
P4  6 P5  6 P6
B)
26
6 C 0  6 C1  6 C 2  6 C 3  6 C 4
D)
26
6
For #16 - 19: Suppose 2 cards are drawn out of a standard deck of cards
without replacement.
16) What is the size of this sample space?
A) 2704
B) 2652
C) 1326
D) 252
17) What is the probability of getting a pair of fours?
12
A)
2704
18)
16
B)
2652
12
C)
2652
16
D)
2704
What is the probability of getting queen and king?
24
A)
2704
32
B)
2652
32
C)
2704
D)
24
2652
19) What is the probability of getting a flush (2 of the same suit)?
624
A)
2652
169
B)
2704
624
C)
2704
D)
156
2652
For #20 – 22: If the probability of giving birth to a boy is 0.52
20) What is the approximate probability of giving birth to four consecutive boys?
A) 0.021
B) 0.062
C) 0.073
D) 0.130
21) What is the approximate probability of giving birth to four consecutive girls?
A) 0.48
B) 0.053
C) 0. 2304
D) 0.111
22) What is the approximate probability of giving birth to exactly two boys?
A) 0.2704
B) 0.062
C) 0. 375
D) 0.374
For # 23 – 24: Abby took an 8-question multiple-choice quiz. Suppose that her
probability of correctly answering any question is 0.75.
23) What is Abby’s probability of incorrectly answering exactly two questions on the
quiz?
A) 0.089
B) 0.240
C) 0.311
D) 0.623
24) What is Abby’s probability of correctly answering exactly half of the quiz
questions?
A) 0.087
B) 0.012
C) 0.316
D) 0.75
25) Given the probability of winning a game is 66%, what are the odds for winning?
A) 17 to 50
B) 33 to 17
C) 17 to 33
D) 50 to 17
26) Given the probability of winning a game is 23%, what are the odds against winning?
A) 23 to 77
B) 23 to 100
C) 100 to 23
D) 77 to 23
27) Given the odds against a runner winning a race is 5 to 4, what is the probability for
the runner winning?
4
A)
5
B)
4
9
C)
5
4
D)
5
9
28) Given the odds of a basketball team winning a tournament is 7 to 9, what is the
probability for the basketball team not winning?
7
A)
16
B)
9
7
C)
9
16
D)
7
9
HONORS DISCRETE PRACTICE MULTIPLE CHOICE
Chapter 15 SOLUTIONS
CHAPTER 15
1. A
12. A
20. C
2. C
13. D
21. B
3. D
14. B
22. D
4. C
15. A
23. C
5. A
16. B
24. A
6. B
17. C
25. B
7. C
18. B
26. D
8. D
19. A
27. B
9. A
10. D
11. C
28. C