Question 13068: Hi, i'm stuck with my homework on math...can anybody help me to figure this out? my question is :
how many ways can 5 people ABCD and E sit in a row if A must be to the left of B but not necessarily next to each other???
thnaks
Answer by kev82(151)   (Show Source):
You can put this solution on YOUR website! Hi,
I found this quite an interesting question, because I couldn't think of a straight forward way to solve it. Obviously a brute force solution is out of the question as there are 120 combinations. This is the best I could come up with:
We know that A must be before B so there are 3 regions in which we can place the other people region p(left of A), q(between A and B), and r(right of B).
p A q B r
We have 3 pieces to place in these regions, the ways we can do that are:
| p | q | r |
|---|
| 3 | 0 | 0 | | 2 | 1 | 0 | | 2 | 0 | 1 | | 1 | 2 | 0 | | 1 | 1 | 1 | | 1 | 0 | 2 | | 0 | 3 | 0 | | 0 | 2 | 1 | | 0 | 1 | 2 | | 0 | 0 | 3 |
In each of these configurations CDE can be assigned any way you like (3! ways) and there are 10 configurations so that makes 10*3!=10*6=60 different ways.
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