AMC12 Combinatorics and Probability 1 — Questions and Answers
Question 1: A committee of 3 is chosen from 7 people. How many ways can this be done?
- 35 (Correct answer)
- 21
- 42
- 28
Correct answer: 35
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?
- 1/3 (Correct answer)
- 1/2
- 2/3
- 1/6
Correct answer: 1/3
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?
- 504 (Correct answer)
- 729
- 648
- 362
Correct answer: 504
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?
- 2/15 (Correct answer)
- 1/5
- 4/15
- 1/3
Correct answer: 2/15
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?
- 1/2 (Correct answer)
- 1/4
- 3/4
- 2/3
Correct answer: 1/2
The outcomes HT and TH each have probability 1/4, giving total P = 1/2.
Question 6: How many ways can 4 books be arranged on a shelf?
- 24 (Correct answer)
- 12
- 16
- 48
Correct answer: 24
4! = 4 × 3 × 2 × 1 = 24.
AMC12 Combinatorics and Probability 1
A committee of 3 is chosen from 7 people.
How many ways can this be done?