Mathematics 9709 · AS & A Level · Permutations and combinations

Permutations and combinations — practice question

A set of $6$ people is to be selected from $4$ men and $11$ women.
(a)[2]

How many different ways are there to choose a group of $6$ if it contains exactly $1$ man?

(b)[3]

How many different ways are there to choose a group of $6$ if Jane and Kate cannot both be in the group? Jane and Kate are two of the $11$ women, and they are sisters.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “A correct combination expression, for instance ${}^{11}C_5\times{}^{4}C_1$” …

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