SOLUTION: 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.

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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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