Practice Test GeeksAMC12 - American Mathematics Competition 12 Practice Test
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Combinatorics & 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.

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  1. In how many ways can 8 people be seated at a round table?

    Answer: 5040

    Circular arrangements of n people = (n-1)! = 7! = 5040.

  2. What is the probability of rolling a sum of 7 with two standard dice?

    Answer: 1/6

    The 6 outcomes summing to 7 give P=6/36=1/6.

  3. How many bit strings of length 8 contain exactly three 1s?

    Answer: 56

    C(8,3)=56.

  4. If a fair die is rolled three times, what is the probability all three rolls are different?

    Answer: 5/9

    P=(6/6)*(5/6)*(4/6)=120/216=5/9.

  5. How many ordered selections of 2 items from 7 are possible (order matters)?

    Answer: 42

    P(7,2)=7*6=42.

  6. How many ways can 5 identical balls be distributed into 3 distinct boxes?

    Answer: 21

    By stars and bars: C(5+3-1,3-1)=C(7,2)=21.