A committee of 6 is chosen from 8 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed?  Choose the correct choice from the following answers.
A) 635 B) 700 C) 1404 D) 2620 E) 3510
The only cases possible are :   1. 2 men and 4 women : 8C2 * 5C4 = 140   2. 3 men and 3 women: 8C3*5C3 = 560   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 = 140+560= 
<gadget id="calculator">140+560</gadget>
<output>700</output>
700. Thus 700 is the correct answer.
<result>B</result>
A committee of 6 is chosen from 8 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed?