SOLUTION: arrange 10 people in a line so that 8 particular people are never together. total no of ways : 10! 8 are always together: 8! So is it 10!-8! ??????

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Question 840115: arrange 10 people in a line so that 8 particular people are never together.
total no of ways : 10!
8 are always together: 8!
So is it 10!-8! ??????
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
arrange 10 people in a line so that 8 particular people are never together.
total no of ways : 10!
8 are always together: 8!
So is it 10!-8! ??????
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Total # of random arrangements = 10!
8 are always together = ?
the block of 8 can be arranged in 8! ways
The block and the 2 remaining people can be arranged in 3! = 6 ways
So # of ways was the 8 to be together is 6*8!
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Ans: 10! - 6*8! = 3386880 ways
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Cheers,
Stan H.
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