Mathematics 9709 · AS & A Level · Permutations and combinations

Permutations and combinations — practice question

A village social club has just been formed and includes 10 members, comprising 6 men and 4 women. The committee of the club is to be made up of 5 members.
(a)[4]

In how many ways may the 5-member committee be selected if it must contain at least 2 men and at least 1 woman?

(b)[2]

How many distinct arrangements of the 10 members are possible if all the men stand together and all the women stand together?

(c)[4]

How many distinct arrangements of the 10 members are there if Olly and Petra must stand next to each other in the front row?

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Uses combinations correctly to count one valid case.

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