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

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(B) committee of $11$ members is to be formed from $8$ males and $5$ females.When at least $6$ males are included,the committee can contain:($6$ males

Vedclass · Accepted Answer

$m=n=78$

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(B) committee of $11$ members is to be formed from $8$ males and $5$ females.When at least $6$ males are included,the committee can contain:($6$ males and $5$ females),($7$ males and $4$ females),or ($8$ males and $3$ females).$m = {}^{8}C_{6} 	imes {}^{5}C_{5} + {}^{8}C_{7} 	imes {}^{5}C_{4} + {}^{8}C_{8} 	imes {}^{5}C_{3}$$m = (28 	imes 1) + (8 	imes 5) + (1 	imes 10) = 28 + 40 + 10 = 78$.When at least $3$ females are included,the committee can contain:($3$ females and $8$ males),($4$ females and $7$ males),or ($5$ females and $6$ males).$n = {}^{5}C_{3} 	imes {}^{8}C_{8} + {}^{5}C_{4} 	imes {}^{8}C_{7} + {}^{5}C_{5} 	imes {}^{8}C_{6}$$n = (10 	imes 1) + (5 	imes 8) + (1 	imes 28) = 10 + 40 + 28 = 78$.Therefore,$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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