Mathematics 9709 · AS & A Level · Permutations and combinations

Permutations and combinations — practice question

A committee made up of 6 people is to be selected from 9 women and 5 men.
(a)[3]

Find how many ways the 6 people may be chosen if the committee must contain more women than men.

(b)[3]

Among the 9 women and 5 men there is a sister and a brother. Find how many ways the committee may be formed if the sister and brother are not allowed to be on the committee at the same time.

Worked solution & mark scheme

This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Valid cases are those with either $5$ or $4$ women, for instance $6W0M$, $5W1M$, $4W2M$” …

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