SOLUTION: In how many ways can 7 people be seated in a row if two of them, Eddie and John, refuse to sit next to each other?

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Question 233615: In how many ways can 7 people be seated in a row if two of them, Eddie and John, refuse to sit next to each other?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
In how many ways can 7 people be seated in a row if two of them, Eddie and John, refuse to sit next to each other?
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Find # of ways to place Eddie and John?
# of ways to put them together = 2*6 = 12
# of ways to put them without restriction: 7C2 = 2*21
Therefore # of ways to seat them not together = 2*21-12 = 30
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# of ways to place the other 5 people = 5!
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Therefore # of ways to meet the problems conditions: 30*5! = 3600
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Cheers,
Stan H.