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

C(7, 3) = 7!/(3! × 4!) = 35.

Question 2

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

Accepted Answer

1/3

Answer

The favorable outcomes are {5, 6}, so probability = 2/6 = 1/3.

Question 3

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

Accepted Answer

504

Answer

9 choices for hundreds, 8 for tens, 7 for units: 9 × 8 × 7 = 504.

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

P = C(4,2)/C(10,2) = 6/45 = 2/15.

Question 5

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

Accepted Answer

1/2

Answer

The outcomes HT and TH each have probability 1/4, giving total P = 1/2.

AMC12 - American Mathematics Competition 12 Practice Test