1. ## Permutation Question

I have the answer but how should it be solved ? This way 1P1*1P1*6P6 ?

Question

7 boys are seated in a row. Calculate different ways in which this can be done if 2 particular boys A and B have exactly 3 other boys between them.

720

2. ## Re: Permutation Question

If B is 3 chairs to the right of A, A can only be seated in chair 1,2, or 3. Otherwise, B is to the left of A, and the possible positions of A and B are switched. That gives 6 possible ways to seat A and B:

A---B--
-A---B-
--A---B
B---A--
-B---A-
--B---A

For each of these ways there are 5! = 120 ways to seat the remaining 5 boys. That gives 6*(5!) = 6! = 720 possible ways to seat the 7 boys under the restrictions listed.