Responding to a pm:
Quote:
4*1*2=8
we have 4 options ( 0,1,2,or 3 employees) for the first office and 1 for the other. Multiply by 2 as we can assign employees to 2nd office first ,in which case 1st office will have only 1 option. Is this reasoning correct?
No, there is a problem in the logic used. There are 4 ways of distributing employees to the 2 offices. The order in which we distribute them in immaterial. So if we have 1 in office 1 and 2 people in office 2, it doesn't matter whether you put the 1 person in first or the 2 people in first. The final distribution is the same hence the logic of multiplying by 2 is nor correct.
Note that when you put 1 person in office 1 and 2 people in office 2, there are 3 distinct ways of doing it since the people are distinct (say A, B and C)
So A in office 1 and B, C in office 2 is different from B in office 1 and A, C in office 2.
So there is 1 way or 0 in office 1 and 3 in office 2.
3 ways of putting 1 in office 1 and 2 in office 2.
3 ways of putting 2 in office 1 and 1 in office 2.
and 1 way of putting 3 in office 1 and 0 in office 2.
That is how you get 1 + 3 + 3 + 1 = 8 cases.
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Karishma
Veritas Prep GMAT Instructor
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