From a group of 10 men and 8 women,the number | vedclass

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(A) Given,a group of $10$ men and $8$ women. We need to form a committee of $8$ members such that there are not more than $5$ men and not less than $5

Vedclass · Accepted Answer

$8061$

Vedclass · Answer

(A) Given,a group of $10$ men and $8$ women. We need to form a committee of $8$ members such that there are not more than $5$ men and not less than $5$ women. This implies the possible combinations of (Women,Men) are: $(5W, 3M), (6W, 2M), (7W, 1M), (8W, 0M)$. The number of ways is calculated as: $= \binom{8}{5} 	imes \binom{10}{3} + \binom{8}{6} 	imes \binom{10}{2} + \binom{8}{7} 	imes \binom{10}{1} + \binom{8}{8} 	imes \binom{10}{0}$ $= (56 	imes 120) + (28 	imes 45) + (8 	imes 10) + (1 	imes 1)$ $= 6720 + 1260 + 80 + 1 = 8061$ ways.

From a group of $10$ men and $8$ women,the number of ways of forming a committee of $8$ members with not more than $5$ men and not less than $5$ women is

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