Exercise 442Combinatorics › Counting principlesHigh schoolAdded 3 Nov 2026

Combinations

#combinations#unordered selection#binomial

Statement

From $10$ students, how many ways can we form a committee of $3$ (order irrelevant)?

Hint

Compute $\binom{10}{3}=\frac{10\cdot9\cdot8}{3\cdot2\cdot1}$ .

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Combination formula. $\binom{10}{3}=\frac{10!}{3!\,7!}=\frac{10\cdot9\cdot8}{6}=120$ .

Conclusion. There are $120$ possible committees.

Remark. $\binom{n}{k}=\frac{n!}{k!(n-k)!}$ .