A department of eleven people - five 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?  Options: A) 250 B) 270 C) 300 D) 320 E) 350
They can make a team of 3 men and 2 women.   The number of ways to do this is 5C3*6C2=10*15= 
<gadget id="calculator">10*15</gadget>
<output>150</output>
150   They can make a team of 2 men and 3 women.   The number of ways to do this is 5C2*6C3=10*20= 
<gadget id="calculator">10*20</gadget>
<output>200</output>
200   The total number of distinct groups is 350.   The answer is 350.
<result>E</result>
A department of eleven people - five 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?