In how many ways can a committee,consisting o | vedclass

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(C) To form the committee,we need to select $5$ men from $8$ and $6$ women from $10$.The number of ways to select $5$ men from $8$ is given by the com

Vedclass · Accepted Answer

$11760$

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

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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