A committee of 6 is chosen from 6 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed?
Answers: A) 275 B) 700 C) 1404 D) 2620 E) 3510
The only cases possible are :   1. 2 men and 4 women : 6C2 * 5C4 = 75   2. 3 men and 3 women: 6C3*5C3 = 200   Rest of the cases will either have 1 or 0 men (not allowed) or will have 1 or 2 or 0 women (not allowed)   Total possible combinations = 75+200= 
<gadget id="calculator">75+200</gadget>
<output>275</output>
275. Thus 275 is the correct answer.
<result>A</result>
A committee of 6 is chosen from 6 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed?