Assignment of positions

Question

 Assume that you have a committee of 15 members, made up of 8 men and 7 women.

In how many ways can the 3 tasks be assigned so that both men and women are given assignments? 

Answer 1

Let's assume that the 3 tasks are distinguishable and not equal, for example president, vice president and secretary.

There are 2 ways to have both men and women selected for 3 positions: we may select 2 men and a woman or one man and 2 women. This can be done C(8,2)*C(7,1) + C(8,1)*C(7,2) number of ways.

Once we have the 3 persons selected we can give them the 3 positions in 3! different ways.

So the final answer is (C(8,2)*C(7,1) + C(8,1))*C(7,2)*(3!)

= (28*7+8*21)*6 = 2184