AMC12 Combinatorics & Probability

Question 1

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

Accepted Answer

120

Answer

The number of permutations of 5 distinct people is 5!=120.

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

3 red balls out of 8 total gives P(red)=3/8.

Question 3

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

Accepted Answer

56

Answer

C(8,3)=8!/(3!5!)=56.

Question 4

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

Accepted Answer

1/6

Answer

There are 6 matching outcomes out of 36 total: P=6/36=1/6.

Question 5

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

Accepted Answer

64

Answer

With 4 choices per position and 3 positions, the total is 4^3=64.

AMC12 - American Mathematics Competition 12 Practice Test