Question 1038067: Ann, Bob, Chris, Dave and Eddy are in a group, how many ways can they be arranged in a row if Ann has to be to the left of Bob but not necessarily beside him.
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
We can choose the pair of positions for A and B to be in
in 5C2 = 10 ways. In each of those 10 ways we can always
put Ann left of Bob. To illustrate, we could have Ann
and Bob in any of the following 5C2 = 10 ways, with Ann
always left of Bob, but not necessarily beside him.
1. A B _ _ _
2. A _ B _ _
3. A _ _ B _
4. A _ _ _ B
5. _ A B _ _
6. _ A _ B _
7. _ A _ _ B
8. _ _ A B _
9. _ _ A _ B
10. _ _ _ A B
Then for each of those 5C2 = 10 ways to place Ann and Bob,
the remaining 3 people can be arranged in the 3 blanks in
3! or 6 ways:
Answer: (5C2)(3!) = (10)(6) = 60 ways.
Edwin
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