AMC12 Combinatorics & Probability

Question 1

In how many ways can 5 people be arranged in a line?

Accepted Answer

120

Answer

60

Answer

24

Answer

240

Question 2

A bag has 3 red and 5 blue balls. One ball is drawn at random. What is P(red)?

Accepted Answer

3/8

Answer

5/8

Answer

1/3

Answer

3/5

Question 3

How many ways can 3 people be chosen from a group of 8?

Accepted Answer

56

Answer

336

Answer

28

Answer

112

Question 4

Two dice are rolled. What is the probability both show the same number?

Accepted Answer

1/6

Answer

1/12

Answer

1/36

Answer

1/3

Question 5

How many 3-letter strings (repetition allowed) can be formed from {A,B,C,D}?

Accepted Answer

64

Answer

24

Answer

48

Answer

12

Question 6

From a 52-card deck, what is the probability of drawing an ace or a king?

Accepted Answer

2/13

Answer

1/13

Answer

4/52

Answer

1/26