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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 or all women?
Correct Answer: B
This is a combinations problem
  1. Since the order in which the group is selected does not matter, we are dealing with a combinations problem (and not a permutations problem).
  2. 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.
  3. The total number of combinations is therefore:
    8!/((8-4)!4!) = 70
  4. However, two of these combinations are not valid since they have all members of one gender.
  5. The correct answer is 70-2 = 68

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