A project manager needs to select a group of 3 people from a total of 3 men and 3 women. How many possible group combinations exist such that no group has all men or all women? Choices:
A) 18	B) 24	C) 74	D) 82	E) 48
Since the order in which the group is selected does not matter, we are dealing with a combinations problem (and not a permutations problem).   The formula for combinations is:   N!/((N-K)!K!)   Where N = the total number of elements from which we will select, 6 people in this case.   Where K = the total number of elements to select, 3 people in this case.   The total number of combinations is therefore:   6!/((6-3)!3!) = 20   However, two of these combinations are not valid since they have all members of one gender.   The correct answer is  20-2= 
<gadget id="calculator"> 20-2</gadget>
<output>18</output>
18. 18ns 18
<result>A</result>
A project manager needs to select a group of 3 people from a total of 3 men and 3 women. How many possible group combinations exist such that no group has all men or all women?