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Question

1) There is a class with 7 men and 13 women that wants to send a delegation of 3 people to see their teacher. How many ways can they form this delegation if there needs to be 2 women and 1 man in the delegation?math 

Answer 1

There are 3 "slots" of which 2 are filled by women and 1 by a man.  Assume the first 2 slots are the women slots.  Then there are 13 women available to fill the first slot, but only 12 women available to fill the second slot, since 1 woman is already accounted for in the first slot.  So far, that is 13 x 12 = 156 ways to fill the 2 women slots.  The third slot is to be filled by a man, and there are 7 men available to fill it.  Then the total number N of ways to fill the 3 slots is the product of the ways to fill each slot:

 

N = (number of ways to fill first woman slot)*(number of ways to fill second woman slot)*(number of ways to fill one man slot)

 

N = 13 x 12 x 7 = 1092 ways