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Question:

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?

m=n=78

m+n=68

n=m-8

m=n=68

Solution:

Since there are 8 males and 5 females. Out of these 13, if we select 11 persons, then there will be at least 6 males and at least 3 females in the selection. m = n = $inom{13}{11} = inom{13}{2} = rac{13 imes 12}{2} = 78$.