Practice Test GeeksAMC12 - American Mathematics Competition 12 Practice Test
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Combinatorics and Probability Flashcards

6 cards from real AMC12 practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 6 Combinatorics and Probability flashcards as text

  1. What is C(8, 3)?

    Answer: 56

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

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

    Answer: 30

    'LEVEL' has 5 letters with L repeated twice and E repeated twice, so arrangements = 5!/(2!2!) = 30.

  3. What is the probability that a card drawn from a standard 52-card deck is a face card or a heart?

    Answer: 11/26

    By inclusion-exclusion: (12 + 13 − 3)/52 = 22/52 = 11/26.

  4. If P(A) = 0.4 and P(B) = 0.3 and A, B are independent, what is P(A ∩ B)?

    Answer: 0.12

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

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

    Answer: 60

    P(5, 3) = 5!/(5−3)! = 5 × 4 × 3 = 60.

  6. A fair coin is flipped 5 times. What is the probability of getting exactly 3 heads?

    Answer: 5/16

    C(5, 3) × (1/2)⁵ = 10/32 = 5/16.