There are 6 men and 8 women in a club in whic | vedclass

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(C) The club consists of $6$ men and $8$ women.We need to form a committee of $5$ people.If no man is selected,all $5$ members of the committee must b

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$56$

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(C) The club consists of $6$ men and $8$ women.We need to form a committee of $5$ people.If no man is selected,all $5$ members of the committee must be chosen from the $8$ women.The number of ways to select $5$ women out of $8$ is given by the combination formula ${}^{n}C_{r} = \frac{n!}{r!(n-r)!}$.Substituting the values,we get ${}^{8}C_{5} = \frac{8!}{5!(8-5)!} = \frac{8!}{5!3!}$.This simplifies to $\frac{8 	imes 7 	imes 6}{3 	imes 2 	imes 1} = 8 	imes 7 = 56$.Thus,there are $56$ ways to form the committee.

There are $6$ men and $8$ women in a club in which a committee of $5$ people has to be formed. What will be the number of ways to select $5$ people if no man is selected?

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