Mathematics 9709 · AS & A Level · Permutations and combinations

Permutations and combinations — practice question

A darts club consists of 12 members: 7 men and 5 women. Each Monday, 4 people are selected at random to represent the club in a competition.
(a)[3]

Find the probability that, on one Monday, the team includes 1 man and 3 women.

(b)[2]

Each Tuesday, the darts club selects 3 teams of 4. Every team takes part in a competition in a different town. How many different ways are there to choose the teams if there are no restrictions?

(c)[3]

How many different ways are there to choose the teams if every team has to include at least 1 man and at least 1 woman?

(d)[2]

The 7 men are lined up for a photograph. Two of them are brothers, George and Harry. How many different arrangements of the 7 men are there if there are exactly 2 men between George and Harry?

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Probability obtained correctly by either sequential fractions or combinations.

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