From a group of 7 men and 6 women,five person | vedclass

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(D) Total number of persons $= 7 + 6 = 13$.We need to select $5$ persons such that at least $3$ are men.This can be done in the following cases:Case $

Vedclass · Accepted Answer

$756$

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(D) Total number of persons $= 7 + 6 = 13$.We need to select $5$ persons such that at least $3$ are men.This can be done in the following cases:Case $1$: $3$ men and $2$ women.Number of ways $= {}^{7}C_{3} 	imes {}^{6}C_{2} = \frac{7 	imes 6 	imes 5}{3 	imes 2 	imes 1} 	imes \frac{6 	imes 5}{2 	imes 1} = 35 	imes 15 = 525$.Case $2$: $4$ men and $1$ woman.Number of ways $= {}^{7}C_{4} 	imes {}^{6}C_{1} = {}^{7}C_{3} 	imes 6 = 35 	imes 6 = 210$.Case $3$: $5$ men and $0$ women.Number of ways $= {}^{7}C_{5} 	imes {}^{6}C_{0} = {}^{7}C_{2} 	imes 1 = \frac{7 	imes 6}{2 	imes 1} = 21$.Total number of ways $= 525 + 210 + 21 = 756$.

From a group of $7$ men and $6$ women,five persons are to be selected to form a committee so that at least $3$ men are there in the committee. In how many ways can it be done?

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