A committee of 6 is chosen from 7 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed?
Pick one.
A) 455 B) 700 C) 1404 D) 2620 E) 3510
The only cases possible are :   1. 2 men and 4 women : 7C2 * 5C4 = 105   2. 3 men and 3 women: 7C3*5C3 = 350   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 = 105+350= 
<gadget id="calculator">105+350</gadget>
<output>455</output>
455. Thus 455 is the correct answer.
<result>A</result>
A committee of 6 is chosen from 7 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed?