SOLUTION: How many way's can 6 people arrange themselve's in a photograph if 2 of them cannot be beside each other?

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Question 1010365: How many way's can 6 people arrange themselve's in a
photograph if 2 of them cannot be beside each other?
Found 3 solutions by stanbon, Edwin McCravy, MathTherapy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
How many way's can 6 people arrange themselve's in a photograph if 2 of them cannot be beside eachother
--------
# of ways they CAN be beside each other:: 4*4! = 4*24 = 96
# of possible arrangements:: 6! = 720
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Ans to the question:: 720-95
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Cheers,
Stan H.
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
The above answer is wrong.

Suppose the 6 people are A,B,C,D,E,F and A and B cannot be together.

There are 6! = 720 ways to arrange the 6 people regardless of 
whether A and B are together or not.

From that we subtract the number of ways where the two are together
with A on the left of B. Then that is the number of ways to arrange 
these 5 things, 1 pair of people and 4 single people.

AB,C,D,E,F

which is 5!

And we also must subtract the number of ways where the two are 
together with B on the left of A. This time the number of ways to 
arrange these 5 things, also 1 pair of people and 4 single people.

BA,C,D,E,F

which is also 5!

So the correct answer is 6! - 5! - 5! = 6! - 2*5! = 480 ways.

Edwin
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

How many way's can 6 people arrange themselve's in a
photograph if 2 of them cannot be beside each other?
1st position: 5 ways

2nd position: 4 ways

3rd position: 4 ways

4th position: 3 ways

5th position: 2 ways

6th position: 1 way



Number of ways: 5 * 4 * 4 * 3 * 2 * 1, or  

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