A committee of 11 members is to be formed fro | vedclass

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(C) Total members to be selected = $11$.Total available members = $8$ men + $5$ women = $13$ members.To select $11$ members out of $13$,we exclude $13

Vedclass · Accepted Answer

$m = n = 78$

Vedclass · Answer

(C) Total members to be selected = $11$.Total available members = $8$ men + $5$ women = $13$ members.To select $11$ members out of $13$,we exclude $13 - 11 = 2$ members.Case $m$ (at least $6$ men): Possible combinations are ($6$$M$,$5$$F$),($7$$M$,$4$$F$),($8$$M$,$3$$F$).$m = \binom{8}{6}\binom{5}{5} + \binom{8}{7}\binom{5}{4} + \binom{8}{8}\binom{5}{3} = (28 	imes 1) + (8 	imes 5) + (1 	imes 10) = 28 + 40 + 10 = 78$.Case $n$ (at least $3$ women): Possible combinations are ($8$$M$,$3$$F$),($7$$M$,$4$$F$),($6$$M$,$5$$F$).$n = \binom{5}{3}\binom{8}{8} + \binom{5}{4}\binom{8}{7} + \binom{5}{5}\binom{8}{6} = (10 	imes 1) + (5 	imes 8) + (1 	imes 28) = 10 + 40 + 28 = 78$.Thus,since $m = 78$ and $n = 78$,we have $m = n = 78$.

$A$ committee of $11$ members is to be formed from $8$ men and $5$ women. If $m$ is the number of ways to form the committee with at least $6$ men and $n$ is the number of ways to form the committee with at least $3$ women,then:

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