A department of nine people - four men and five women - needs to send a team of five to a conference. If they want to make sure that there are no more than three members of the team from any one gender, how many distinct groups are possible to send? Choices:	A) 100	B) 120	C) 150	D) 180	E) 200
They can make a team of 3 men and 2 women.   The number of ways to do this is 4C3*5C2=4*10= 
<gadget id="calculator">4*10</gadget>
<output>40</output>
40   They can make a team of 2 men and 3 women.   The number of ways to do this is 4C2*5C3=6*10= 
<gadget id="calculator">6*10</gadget>
<output>60</output>
60   The total number of distinct groups is 100.   The answer is 100.
<result>A</result>
A department of nine people - four men and five women - needs to send a team of five to a conference. If they want to make sure that there are no more than three members of the team from any one gender, how many distinct groups are possible to send?