SOLUTION: Solve: 3n(n-2)!/(n-3)=105 Solve for "n" State any restrictions. Thank you!

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Question 594526: Solve: 3n(n-2)!/(n-3)=105 Solve for "n" State any restrictions.

Thank you!
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
, Divide through by 3



We can write n(n-2)! as n!/(n-1). Above equation is equivalent to

or

Here it is obvious that n should be fairly small (at most 8 because (8-4)! = 24). However, n must be at least 7 (because n(n-2)(n-4)! ≡ 0 (mod 7)). Therefore there are no solutions.