A committee of 3 men and 3 women must be formed from a group of 6 men and 8 women. How many such committees can we form if 1 man and 1 woman refuse to serve together?  Pick
A) 610
B) 710
C) 810
D) 910
E) 1010
The number of committees with John but not Mary:(1∗C52)(C73)=10∗35=350;   The number of committees with Mary but not John: (C53)(1∗C72)=10∗21=210;   The number of committees without John and without Mary: (C53)(C73)=10∗35=350.   Total = 350 + 350 + 210= 
<gadget id="calculator">350 + 350 + 210</gadget>
<output>910</output>
910.   ANSWER:910
<result>D</result>
A committee of 3 men and 3 women must be formed from a group of 6 men and 8 women. How many such committees can we form if 1 man and 1 woman refuse to serve together?