There are 6 Men and 8 Women in a club in whic | vedclass

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Question

(C) At most one man means either no man is selected or exactly one man is selected.Case $1$: No man is selected.This means all $5$ members are selecte

Vedclass · Accepted Answer

$476$

Vedclass · Answer

(C) At most one man means either no man is selected or exactly one man is selected.Case $1$: No man is selected.This means all $5$ members are selected from $8$ women.Number of ways $= {}^{8}C_{5} = \frac{8 	imes 7 	imes 6}{3 	imes 2 	imes 1} = 56$.Case $2$: Exactly one man is selected.This means $1$ man is selected from $6$ men and $4$ women are selected from $8$ women.Number of ways $= {}^{6}C_{1} 	imes {}^{8}C_{4} = 6 	imes \frac{8 	imes 7 	imes 6 	imes 5}{4 	imes 3 	imes 2 	imes 1} = 6 	imes 70 = 420$.Total number of ways $= 56 + 420 = 476$.

There are $6$ Men and $8$ Women in a club in which a committee of $5$ people has to be made. What will be the number of ways to select $5$ people if at most one man is selected?

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