Six married couples decide to form a committe | vedclass

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(B) We have $6$ married couples,which means a total of $12$ people.To form a committee of $6$ persons such that no couple is included,we must first se

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$64$

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(B) We have $6$ married couples,which means a total of $12$ people.To form a committee of $6$ persons such that no couple is included,we must first select $6$ couples out of the $6$ available couples. This can be done in $\binom{6}{6} = 1$ way.From each of the $6$ selected couples,we must choose exactly one person to be on the committee. Since each couple has $2$ members,there are $2$ choices for each of the $6$ positions.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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