a department of 10 people - 6 men and 4 women - needs to send a team of 5 to a conference. if they want to make sure that there are no more than 3 members of the team from any one gender, how many distinct groups are possible to send? Choose the correct option:  A) 120  B) 150  C) 180  D) 210  E) 240
<gadget id="calculator">6 * 5</gadget>
<output>30</output>

<gadget id="calculator">30 * 4</gadget>
<output>120</output>

<gadget id="calculator">120 + 30</gadget>
<output>150</output>

<gadget id="calculator">150 + 30</gadget>
<output>180</output>

<result>C</result>
a department of 10 people - 6 men and 4 women - needs to send a team of 5 to a conference. if they want to make sure that there are no more than 3 members of the team from any one gender, how many distinct groups are possible to send?
add(add(multiply(multiply(6, 5), 4), multiply(6, 5)), multiply(6, 5))
they can make a team of 3 men and 2 women . the number of ways to do this is 6 c 3 * 4 c 2 = 20 * 6 = 120 they can make a team of 2 men and 3 women . the number of ways to do this is 6 c 2 * 4 c 3 = 15 * 4 = 60 the total number of distinct groups is 180 . the answer is c .