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:

Step-by-step solution

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 .