Six married couples decide to form a committe | vedclass

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(B) There are $6$ married couples,so there are $12$ people in total.We need to select $6$ people out of $12$ such that no two people form a couple.Fir

Vedclass · Accepted Answer

$64$

Vedclass · Answer

(B) There are $6$ married couples,so there are $12$ people in total.We need to select $6$ people out of $12$ such that no two people form a couple.First,we select $6$ couples out of $6$ available couples,which can be done in $\binom{6}{6} = 1$ way.From each of these $6$ selected couples,we must choose exactly one person to be on the committee.Since each couple has $2$ people,for each of the $6$ positions,we have $2$ choices.Therefore,the total number of ways is $\binom{6}{6} 	imes 2^6 = 1 	imes 64 = 64$.

Six married couples decide to form a committee of $6$ persons. The total number of ways to form the committee such that it contains no couples is equal to:

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