This question is about six couples. Each couple consists of a husband and wife. The $12$ people vi

Question

This question is about six couples. Each couple consists of a husband and wife.

The $12$ people visit a theatre, and sit in a row of $12$ seats.

In how many different ways can the $12$ people sit so that each husband and wife in a couple sit next to each other?[2]
In how many different ways can the $12$ people sit so that the $6$ wives all sit next to each other, and none of the wives sits next to her own husband?[3]

The group decides to form a committee to arrange future outings. The committee will consist of $3$ of the $12$ people.
At least 1 of the wives will be on the committee but no husband and wife couple will be included.

In how many ways can the committee be formed?[3]

Accepted Answer

(i) $46\,080$ (ii) $2\,678\,400$ (iii) $140$

2017 Specimen Paper P2 Q5

2017 Specimen Paper P2 Q5

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