There are 7 men and 8 women in a club. A comm | vedclass

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Question

(A) Total number of people in the club $= 7 + 8 = 15$.Total number of ways to select $6$ persons out of $15$ is given by ${}^{15}C_6$.${}^{15}C_6 = \f

Vedclass · Accepted Answer

$4998$

Vedclass · Answer

(A) Total number of people in the club $= 7 + 8 = 15$.Total number of ways to select $6$ persons out of $15$ is given by ${}^{15}C_6$.${}^{15}C_6 = \frac{15 	imes 14 	imes 13 	imes 12 	imes 11 	imes 10}{6 	imes 5 	imes 4 	imes 3 	imes 2 	imes 1} = 5005$.To find the number of ways such that at least one woman is selected,we subtract the number of ways where no woman is selected (i.e.,all $6$ are men) from the total number of ways.Number of ways to select $6$ men out of $7$ is ${}^{7}C_6$.${}^{7}C_6 = {}^{7}C_1 = 7$.Required number of ways $= {}^{15}C_6 - {}^{7}C_6 = 5005 - 7 = 4998$.

There are $7$ men and $8$ women in a club. $A$ committee is formed using these persons. What will be the number of ways to select $6$ persons such that at least one is a woman?

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