A department of ten people - four men and six 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?
Pick.
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*6C2=4*15= 
<gadget id="calculator">4*15</gadget>
<output>60</output>
60   They can make a team of 2 men and 3 women.   The number of ways to do this is 4C2*6C3=6*20= 
<gadget id="calculator">6*20</gadget>
<output>120</output>
120   The total number of distinct groups is 180.   The answer is 180.
<result>D</result>
A department of ten people - four men and six 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?