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Four couples (husband and wife)decide to form a committee of four members. How many committees can be formed so that no couple finds a place in it?

1 Answer

The required committee can have
1. all men = $^4C_4=1$ or
2. all women =$^4C_4=1$ or
3. three men and 1 woman who is not the wife of any of the three men.
$=^4C_3\times ^1C_1=4$ or
4. three women and one men who is not the husband of the three women.
$=^4C_3\times ^1C_1=4$ or
5. two men and two women who are not the wives of the selected men.
$=^4C_2\times ^2C_2=6$
$\therefore$ The required no. of committees = $1+1+4+4+6=16$
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