A department of ten people - six men and four 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?  Choose the most appropriate option:
A) 120 B) 150 C) 180 D) 210 E) 240
They can make a team of 3 men and 2 women.   The number of ways to do this is 6C3*4C2=20*6= 
<gadget id="calculator">20*6</gadget>
<output>120</output>
120   They can make a team of 2 men and 3 women.   The number of ways to do this is 6C2*4C3=15*4= 
<gadget id="calculator">15*4</gadget>
<output>60</output>
60   The total number of distinct groups is 180.   The answer is 180.
<result>C</result>
A department of ten people - six men and four 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?