FREE AMC 12 Combinatorics & Probability Questions and Answers

Question 1

How many ways can you arrange the letters of the word 'MATH'?

Accepted Answer

24

Answer

12

Answer

16

Answer

8

Question 2

What is the probability of rolling a sum of 7 with two fair dice?

Accepted Answer

1/6

Answer

1/12

Answer

1/36

Answer

1/9

Question 3

How many different ways can you select 3 objects from a set of 10?

Accepted Answer

120

Answer

45

Answer

30

Answer

60

Question 4

What is the probability of drawing a red card from a standard deck of 52 cards?

Accepted Answer

1/2

Answer

1/4

Answer

1/3

Answer

1/5

Question 5

If a fair coin is tossed 3 times, what is the probability of getting exactly 2 heads?

Accepted Answer

3/8

Answer

1/4

Answer

1/2

Answer

1/8

Question 6

How many different ways can you arrange 3 blue balls, 2 red balls, and 1 green ball?

Accepted Answer

60

Answer

120

Answer

24

Answer

30

Question 7

In how many ways can you distribute 5 identical objects into 3 distinct boxes?

Accepted Answer

21

Answer

15

Answer

10

Answer

25

Question 8

What is the number of ways to arrange the digits 1, 2, 3, 4, and 5 in a 5-digit number?

Accepted Answer

120

Answer

60

Answer

24

Answer

30

Question 9

If a fair die is rolled, what is the probability of rolling an even number?

Accepted Answer

1/2

Answer

1/6

Answer

1/3

Answer

1/4