A project manager needs to select a group of 4 people from a total of 4 men and 4 women. How many possible group combinations exist such that no group has all men ?  Choose one.
A) 72 B) 68 C) 74 D) 82 E) 69
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, 8 people in this case.   Where K = the total number of elements to select, 4 people in this case.   The total number of combinations is therefore:   8!/((8-4)!4!) = 70   However, one of these combinations are not valid since they have all members of men   The correct answer is  70-1= 
<gadget id="calculator"> 70-1</gadget>
<output>69</output>
69.Ans 69
<result>E</result>
A project manager needs to select a group of 4 people from a total of 4 men and 4 women. How many possible group combinations exist such that no group has all men ?