From a group of 8 men and 7 women, a committee consisting of 4 men and 5 women is to be formed. A group of 3 men refuses to serve together (each in this group won't serve with either one or both others).

How many different committees are possible?

a. none of the answers provided here

b. 735

c. 4785

d. 105

e. 1365

Answer: Option E.

Step-by-step explanation:

The total number of committees possible if no conditions persists is=

⁸C₄ x ⁷C₅ = 70 x 21 = 1470

Now, 3 men refuse to serve together

So, combination possible for the scenario when they serve together is = ⁵C₄ x ⁷C₅ = 5 x 21 = 105

So, combination possible for the scenario when they don't servce together is = 1470 - 105 = 1365