A group has 6 men and 5 women. How many ways can a committee of 2 men and 4 women be formed?
Emily:
You can choose the 2 men on the committee from the 6 men in the group in ^{
6}C_{2} = (6!) / (2!) (4!) = 6x5 / 2 = 15 ways and you can choose the 4 women on the committee from the 5 women in the group in
^{5}C_{4} = (5!) / (4!)(1!) = 5 ways. So the total number of ways such a committee can be formed is 15 x 5 = 75.
Dattaprabhakar (Dr. G.)