Probability - P(n,5) = 20P (n,3)

Hi could someone please help me with the following problem from a Grade 12 Data Management course..


P(n,5) = 20P (n,3)

This is my answer so far...

n! ÷ (n-5)! = 20 n! ÷ (n-3)!
n(n-1)(n-2)(n-3)(n-4) = 20 n(n-1)(n-2)
Divide by n(n-1)(n-2)

(n-3)(n-4)=20
n^2 - 7n + 12= 20
n^2- 7n - 8 =0
(n-4)(n+2) = 0

Then i am confused.. I do not think this is right. Please help!

You factored incorrectly.
\(\displaystyle n^2 -7n -8 = (n+1)(n-8)\)