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Combinatorics and Counting Flashcards

6 cards from real IMO 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. What is C(6, 2)?

    Answer: 15

    C(6,2) = 6!/(2! × 4!) = (6 × 5)/(2 × 1) = 15.

  2. A die is rolled once. What is the probability of getting an even number?

    Answer: 1/2

    Even numbers on a die: 2, 4, 6 — that's 3 out of 6; probability = 3/6 = 1/2.

  3. How many 4-letter codes can be made from 26 letters if repetition is allowed?

    Answer: 26⁴

    With repetition allowed, each of the 4 positions has 26 choices: total = 26⁴ = 456,976.

  4. In how many ways can 4 people be seated in a row of 4 chairs?

    Answer: 24

    This is 4! = 4 × 3 × 2 × 1 = 24.

  5. A bag has 5 red and 3 blue balls. What is the probability of picking a blue ball?

    Answer: 3/8

    Total balls = 8; P(blue) = 3/8.

  6. How many ways can a team of 3 be selected from 7 players?

    Answer: 35

    C(7,3) = 7!/(3! × 4!) = (7 × 6 × 5)/(3 × 2 × 1) = 35.

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Sources & references

Exam facts on this page (fees, format, dates, passing scores) are checked against these official sources; the date is our last check. Editorial policy

  1. imo-official.org — Test delivery, eligibility, passing score, test dates, exam format · verified Oct 2026
  2. imo2027.hu — Exam dates, registration deadline · verified Oct 2026