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 if two of the men refuse to serve together?
Choices.
A) 3510
B) 2620
C) 1404
D) 700
E) 635
Committee can have either: 2 men and 4 women OR 3 men and 3 women (to meet the condition of at least 2 men and 3 women).   Ways to chose 6 members committee without restriction (two men refuse to server together): C28∗C45+C38∗C35=700C82∗C54+C83∗C53=700   Ways to chose 6 members committee with two particular men serve together: C22∗C45+(C22∗C16)∗C35=5+60= 
<gadget id="calculator">5+60</gadget>
<output>65</output>
65C22∗C54+(C22∗C61)∗C53=5+60= 
<gadget id="calculator">5+60</gadget>
<output>65</output>
65   700-65= 
<gadget id="calculator">700-65</gadget>
<output>635</output>
635   Answer: 635.
<result>E</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 if two of the men refuse to serve together?