A group of 6 is chosen from 8 men and 5 women so as to

Groupings can be (2 men, 4 women) or (3 men, 3 women)


Consider (2men, 4 women)
We have 8 men, but two refuse to work together. Number of ways these 2 men can work together is 1. Total number of ways to pick 2 men from 8 = 8C2 = 28. So number of ways to pick 2 men without two of them in the same team = 27.

Number of ways to pick 4 women = 5C4 = 5.
Total number of combinations for 2men, 4women team = 5 *27 = 135

Consider (3men, 3women)
Number of ways the two men who refuse to work together are picked = 6 (2 of them + match with any 6 others remaining). Number of ways to pick 3 men from = 8C3 = 56. So number of ways to pick 3 men without two of them in the same team = 56-6 = 50

Number of ways to pick 3 women = 5C3 = 10
Total number of combinations for 3men, 3women team = 500

Total number of possibilities = (2men, 4women team) OR (3men, 2 women team) = 135+500 = 635

agreed E is the answer.