please help!!!!?

Question

solve for n

http://i150.photobucket.com/albums/s83/kagemushaf/problem.jpg

please explain, thank you

Answer 1

This is a question about permutations. To have P(12, n) = P(12, 2n), the first obvious answer is n = 0, because then 2n = 0 as well, so you have P(12, 0) = P(12, 0), which is clearly true. It takes some analysis to determine if there is another answer. P(r, n) = n! / (n - r)!, so P(12, n) = 12! / (12 - n)! and we therefore need 12! / (12 - n)! = 12! / (12 - 2n)! ==> 12!*(12 - 2n)! = 12!*(12 - n)! ==> (12 - 2n)! = (12 - n)! ==> 12 - 2n = 12 - n ==> n = 0, the answer we already had. So this equation is only true if n = 0. If we were looking for combinations instead of permutations, I believe n = 4 would also have been a solution.

Answer 2

I'm either going to do this totally right or totally wrong, depending on if I remember what that P symbol ment (but I think I'm pretty right)

Basically, it's 12!/n!=12!/2n!
By cross multiplying, that's 12!n!=12!2n!
By dividing 12 from both sides, that is n!=2n!

And the only thing that I know of that works for that would be 0...