A committee of 11 member 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 a

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A committee of 11 member 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:

TestHub · Accepted Answer

m = ( 6 M , 5 F ) + ( 7 M , 4 F ) + ( 8 M , 3 F ) = C 6 8 × C 5 5 + C 7 8 × C 4 5 + C 8 8 × C 3 5 = 28 × 1 + 8 × 5 + 1 × 10 = 78 n = ( 3 F , 8 M ) + ( 4 F , 7 M ) + ( 5 F , 6 M ) = C 3 5 × C 8 8 + C 4 5 × C 7 8 + C 5 5 × C 6 8 = 10 × 1 + 5 × 8 + 1 × 28 = 78 Hence, m = n = 78 .

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