FoundationNumeric answerFree solution

How many ways can a committee of 33 be chosen from 88 people?

Answer with a number. Fractions, powers and expressions like 23/6 or C(52,5) are read correctly in practice.

Show the answer and worked solution

Answer

5656

Classify first: the committee is unordered and nobody serves twice, so it is a combination. (83)=8×7×63×2×1=3366=56\binom{8}{3} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = \frac{336}{6} = 56. Cancelling as you go rather than expanding 8!8! is the habit worth building, since the factorials get unmanageable fast. A quick check: (83)=(85)\binom{8}{3} = \binom{8}{5} by symmetry, and both count the same split of eight people into three and five.

Worked solution

  1. Formula
    (nk)=n!k!(n−k)!\binom{n}{k} = \frac{n!}{k!(n-k)!}
  2. Substitute
    =8×7×63×2×1= \frac{8 \times 7 \times 6}{3 \times 2 \times 1}
  3. Solve
    =3366= \frac{336}{6}
  4. Answer
    5656

Takeaway: Order does not matter and nothing repeats, so it is a binomial coefficient.

Answer it in practice – your answer is marked and recorded.

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