2017 Specimen Paper P2 Q5
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.
(i)
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]
(ii)
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.
(iii)
In how many ways can the committee be formed?
[3]
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