A committee of 6 is chosen from 8 men and 4 women so as to contain at least 2 men and 3 women. How many different committees could be formed? Pick one:	A) 252	B) 700	C) 1404	D) 2620	E) 3510
The only cases possible are :   1. 2 men and 4 women : 8C2 * 4C4 = 28   2. 3 men and 3 women: 8C3*4C3 = 224   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 = 28+224= 
<gadget id="calculator">28+224</gadget>
<output>252</output>
252. Thus 252 is the correct answer.
<result>A</result>
A committee of 6 is chosen from 8 men and 4 women so as to contain at least 2 men and 3 women. How many different committees could be formed?