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 ?
Choose the correct choice from the following answers.
A) 72  B) 68  C) 24  D) 19  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, one of these combinations are not valid since they have all members of men   The correct answer is  20-1= 
<gadget id="calculator"> 20-1</gadget>
<output>19</output>
19. Ans 19
<result>D</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 ?