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. A committee of 3 is chosen from 7 people. How many ways can this be done?

    Answer: 35

    C(7, 3) = 7!/(3! × 4!) = 35.

  2. A fair die is rolled. What is the probability of getting a number greater than 4?

    Answer: 1/3

    The favorable outcomes are {5, 6}, so probability = 2/6 = 1/3.

  3. How many 3-digit numbers can be formed from digits 1–9 without repetition?

    Answer: 504

    9 choices for hundreds, 8 for tens, 7 for units: 9 × 8 × 7 = 504.

  4. A bag has 4 red and 6 blue balls. What is the probability of drawing 2 red balls without replacement?

    Answer: 2/15

    P = C(4,2)/C(10,2) = 6/45 = 2/15.

  5. Two fair coins are flipped. What is the probability of getting exactly one head?

    Answer: 1/2

    The outcomes HT and TH each have probability 1/4, giving total P = 1/2.

  6. How many ways can 4 books be arranged on a shelf?

    Answer: 24

    4! = 4 × 3 × 2 × 1 = 24.