A committee of 7 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?	Options:  A) 308  B) 700  C) 1404  D) 2620  E) 3510
The only cases possible are :   1. 2 men and 5 women : 8C2 * 5C5 = 28   2. 4 men and 3 women: 8C4*5C3 = 280   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+280= 
<gadget id="calculator">28+280</gadget>
<output>308</output>
308. Thus 308 is the correct answer.
<result>A</result>
A committee of 7 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?