AMC12 Combinatorics & Probability 1 — Questions and Answers
Question 1: In how many ways can 5 people be arranged in a line?
- 60
- 24
- 240
- 120 (Correct answer)
Correct answer: 120
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)?
- 5/8
- 1/3
- 3/5
- 3/8 (Correct answer)
Correct answer: 3/8
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?
- 336
- 28
- 112
- 56 (Correct answer)
Correct answer: 56
C(8,3)=8!/(3!5!)=56.
Question 4: Two dice are rolled. What is the probability both show the same number?
- 1/12
- 1/36
- 1/3
- 1/6 (Correct answer)
Correct answer: 1/6
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}?
- 24
- 48
- 12
- 64 (Correct answer)
Correct answer: 64
With 4 choices per position and 3 positions, the total is 4^3=64.
Question 6: From a 52-card deck, what is the probability of drawing an ace or a king?
- 1/13
- 4/52
- 1/26
- 2/13 (Correct answer)
Correct answer: 2/13
8 favorable cards (4 aces + 4 kings) out of 52 gives 8/52=2/13.
AMC12 Combinatorics & Probability 1
In how many ways can 5 people be arranged in a line?