AMC12 Combinatorics and Probability 2

Question 1

What is C(8, 3)?

Accepted Answer

56

Answer

C(8, 3) = 8 × 7 × 6 / (3 × 2 × 1) = 336/6 = 56.

Question 2

In how many ways can the letters of 'LEVEL' be arranged?

Accepted Answer

30

Answer

'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?

Accepted Answer

11/26

Answer

By inclusion-exclusion: (12 + 13 − 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 ∩ B)?

Accepted Answer

0.12

Answer

For independent events, P(A ∩ B) = P(A) × P(B) = 0.4 × 0.3 = 0.12.

Question 5

How many ways can 3 people be seated in a row of 5 chairs?

Accepted Answer

60

Answer

P(5, 3) = 5!/(5−3)! = 5 × 4 × 3 = 60.

AMC12 - American Mathematics Competition 12 Practice Test