In how many ways can a committee consisting o | vedclass

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Question

(C) The number of ways to select $5$ men from $8$ men is given by the combination formula ${}^{n}C_{r} = \frac{n!}{r!(n-r)!}$.${}^{8}C_{5} = \frac{8!}

Vedclass · Accepted Answer

$11760$

Vedclass · Answer

(C) The number of ways to select $5$ men from $8$ men is given by the combination formula ${}^{n}C_{r} = \frac{n!}{r!(n-r)!}$.${}^{8}C_{5} = \frac{8!}{5!3!} = \frac{8 	imes 7 	imes 6}{3 	imes 2 	imes 1} = 56$.The number of ways to select $6$ women from $10$ women is ${}^{10}C_{6}$.${}^{10}C_{6} = {}^{10}C_{4} = \frac{10 	imes 9 	imes 8 	imes 7}{4 	imes 3 	imes 2 	imes 1} = 210$.To find the total number of ways to form the committee,we multiply the number of ways to select the men and the women:Total ways $= 56 	imes 210 = 11760$.

In how many ways can a committee consisting of $5$ men and $6$ women be formed from $8$ men and $10$ women?

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