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

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(C) Total members available are $8$ males and $5$ females,so total persons = $13$. We need to select $11$ members.For $m$ (at least $6$ males):Possibl

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$m = n = 78$

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(C) Total members available are $8$ males and $5$ females,so total persons = $13$. We need to select $11$ members.For $m$ (at least $6$ males):Possible cases are ($6$ males,$5$ females),($7$ males,$4$ females),($8$ males,$3$ females).$m = \binom{8}{6} 	imes \binom{5}{5} + \binom{8}{7} 	imes \binom{5}{4} + \binom{8}{8} 	imes \binom{5}{3} = (28 	imes 1) + (8 	imes 5) + (1 	imes 10) = 28 + 40 + 10 = 78$.For $n$ (at least $3$ females):Possible cases are ($8$ males,$3$ females),($7$ males,$4$ females),($6$ males,$5$ females).$n = \binom{5}{3} 	imes \binom{8}{8} + \binom{5}{4} 	imes \binom{8}{7} + \binom{5}{5} 	imes \binom{8}{6} = (10 	imes 1) + (5 	imes 8) + (1 	imes 28) = 10 + 40 + 28 = 78$.Thus,$m = n = 78$.

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

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