AMC12 Combinatorics and Probability

Question 1

A committee of 3 is chosen from 7 people. How many ways can this be done?

Accepted Answer

35

Answer

21

Answer

42

Answer

28

Question 2

A fair die is rolled. What is the probability of getting a number greater than 4?

Accepted Answer

1/3

Answer

1/2

Answer

2/3

Answer

1/6

Question 3

How many 3-digit numbers can be formed from digits 1–9 without repetition?

Accepted Answer

504

Answer

729

Answer

648

Answer

362

Question 4

A bag has 4 red and 6 blue balls. What is the probability of drawing 2 red balls without replacement?

Accepted Answer

2/15

Answer

1/5

Answer

4/15

Answer

1/3

Question 5

Two fair coins are flipped. What is the probability of getting exactly one head?

Accepted Answer

1/2

Answer

1/4

Answer

3/4

Answer

2/3

Question 6

How many ways can 4 books be arranged on a shelf?

Accepted Answer

24

Answer

12

Answer

16

Answer

48