AMC12 Combinatorics and Probability 2 ā Questions and Answers
Question 1: What is C(8, 3)?
- 56 (Correct answer)
- 40
- 70
- 35
Correct answer: 56
C(8, 3) = 8 Ć 7 Ć 6 / (3 Ć 2 Ć 1) = 336/6 = 56.
Question 2: In how many ways can the letters of 'LEVEL' be arranged?
- 30 (Correct answer)
- 60
- 20
- 120
Correct answer: 30
'LEVEL' has 5 letters with L repeated twice and E repeated twice, so arrangements = 5!/(2!2!) = 30.
Question 3: What is the probability that a card drawn from a standard 52-card deck is a face card or a heart?
- 11/26 (Correct answer)
- 25/52
- 22/52
- 9/26
Correct answer: 11/26
By inclusion-exclusion: (12 + 13 ā 3)/52 = 22/52 = 11/26.
Question 4: If P(A) = 0.4 and P(B) = 0.3 and A, B are independent, what is P(A ā© B)?
- 0.12 (Correct answer)
- 0.58
- 0.70
- 0.07
Correct answer: 0.12
For independent events, P(A ā© B) = P(A) Ć P(B) = 0.4 Ć 0.3 = 0.12.
Question 5: How many ways can 3 people be seated in a row of 5 chairs?
- 60 (Correct answer)
- 30
- 120
- 20
Correct answer: 60
P(5, 3) = 5!/(5ā3)! = 5 Ć 4 Ć 3 = 60.
Question 6: A fair coin is flipped 5 times. What is the probability of getting exactly 3 heads?
- 5/16 (Correct answer)
- 1/4
- 3/8
- 1/8
Correct answer: 5/16
C(5, 3) Ć (1/2)āµ = 10/32 = 5/16.
AMC12 Combinatorics and Probability 2
What is C(8, 3)?