SOLUTION: Ten students are to sit on a bench. If two particular student must not sit next to each other, how many sitting arrangement are possible?

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Question 730191: Ten students are to sit on a bench. If two particular student must not sit next to each other, how many sitting arrangement are possible?
Found 2 solutions by lynnlo, ikleyn:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by ikleyn(53411) About Me  (Show Source):
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Ten students are to sit on a bench. If two particular student must not sit next to each other,
how many sitting arrangement are possible?
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With no restrictions, 10! = 10*9*8*7*6*5*4*3*2*1 = 3628800 permutations/arrangements are possible.


With the restriction, we consider the pair of particular students as one block/item.


So, there are 2*9! different unwanted arrangements.


The factor 2 appeared since, two particular students can be ordered in 2 different ways.


So, the number of allowed arrangements is  10! - 2*9! = 3628800 - 2*(9*8*7*6*5*4*3*2*1) = 2903040.


ANSWER.  The number of allowed arrangements is  2903040.

Solved.