How many ways can a committee of 3 people be chosen out of 7 people?

The correct answer is Option (2) → 35

In a committee only the choice of members matters, not their order, so the number of ways is a combination: \({}^{n}C_{r}=\frac{n!}{r!\,(n-r)!}\).

• \(\displaystyle {}^{7}C_{3}=\frac{7!}{3!\,4!}=\frac{7\times6\times5}{3\times2\times1}=35\)

Tip: 210 (Option 3) is \({}^{7}P_{3}=7\times6\times5\), which counts each group of three once for every one of its \(3!=6\) orders; it would fit only if the three places in the committee were different posts.