A department of ten people - five 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? Answers.
A) 100 B) 126 C) 200 D) 252 E) 288
We are given 5 men and 5 Women, out of which we need to select 5 People such that no more than 3 of any gender are selected.   So, We can have Either 3 Men + 2 Women Selected or 2 Men + 3 Women Selected.   Thus, Number of ways for selecting 3 Men + 2 Women = 5C3 * 5C2 = 10*10= 
<gadget id="calculator">10*10</gadget>
<output>100</output>
100   AND Number of ways for selecting 2 Men + 3 Women= 5C2 * 5C3 = 10*10= 
<gadget id="calculator">10*10</gadget>
<output>100</output>
100   Thus, total ways to get the distinct groups will be   100+100= 
<gadget id="calculator">  100+100</gadget>
<output>200</output>
200.   Hence, Ans will be 200.
<result>C</result>
A department of ten people - five 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?