SOLUTION: how many ways can 10 people sit in their seats if say person 3 can't sit between person 1 and 2

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Question 827728: how many ways can 10 people sit in their seats if say person 3 can't sit between person 1 and 2
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
  %22%22=%22%22  %22%22-%22%22%22%22-%22%22


 %22%22=%22%22 10%21 %22%22=%22%22 3628800


 %22%22=%22%22 8%21 %22%22=%22%22 40320

Explanation:
We consider the "trio" (persons 1,3,2 in that order) as 1 single "thing" and
that there are 8 "things", 7 single people and 1 "trio".  That's 8! ways.

 %22%22=%22%22 8%21 %22%22=%22%22 40320

Explanation:
Just like the preceding case, we consider the "trio" (persons 2,3,1 in that
order) as 1 single "thing" and that there are 8 "things", 7 single people and
1 "trio".  That's also 8! or 40320 ways.

Answer:  10! - 2×8! = 3628800 - 2×40320 = 3548160 ways.

Edwin