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
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# 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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