a) In how many ways can a Committee of 4 be formed from a group of 5 men and 6 women in such a way that the men are the majority?

Question

from the  four groups formed men should be majority  in each  group 

 

Answer 1

The men-in-the-majority possibilities are: all 4 are men, or 3 are men.

 

Case 1 (4 men): 5C4 = 5 ways

Case 2(3 men, 1 woman): 5C3•6C1 = 10•6 = 60.

 

Total: 65 ways.