Permutations and Combinations

Question

A committee of 6 members is to be chosen from 6 women and 5 men. Calculate the number of ways this can be done if

a minimum of 4 men must be chosen.

 

Ans:81

Answer 1

There's two different ways this can be done: 4 men + 2 women or 5 men and 1 woman.  So we need to count the number of combos of each and then add them together.

 

5C4 * 6C2    ###the number of ways in which 4 out of 5 possible men and 2 out of 6 possible women can be picked

= 5 * 15

= 75

 

 

5C5 * 6C1   ###the number of ways in which 5 out of 5 possible men and 1 out of 6 possible women can be picked

=1 * 6

=6

 

75 + 6 = 81