solve for n P(n,3) = 60

Question

luigi0210 · Answer

I'm assuming the P means Permutations.. do you know the formula?

anonymous · Answer

yes

anonymous · Answer

P(n,r) = n!/(n-r)!

luigi0210 · Answer

So I'm assuming they want us to work backwards.. 

$\large P(n, r ) = 60 = \frac{n!}{(n-3)!}$ 

And we know that that $n> 3 $

anonymous · Answer

yeah, for sure :)

luigi0210 · Answer

I don't think they'd make the problem too difficult.. so I'd suggest just plugging in values for n that are greater than 3. 

So if we try 4; 4! would equal 24, which is too small and not equal to 60. So 4 won't work. 

Now trying 5: $\large P(5, 3)  = \frac{5!}{(5-3)!} = \frac{120}{2!}$ 

And what's 120/2?

anonymous · Answer

how to solve this then? i'm required to show a solution

anonymous · Answer

$$0=n ^{3}-3n ^{2}+2n-60$$

anonymous · Answer

i have went all until this equation, and i'm stuck

anonymous · Answer

but 5's gonna work for that equation for sure

luigi0210 · Answer

I'm not sure if they want you to go into it that deep, I think just plugging in values would  suffice

anonymous · Answer

yeah they do! and it's HORRIBLE

anonymous · Answer

but thanks anyway :)