Question

find n if npr4=132×npr2

Answer 1

Answer:

n = 14

Step-by-step explanation:

nP4 = 132 ( nP2 )

n! /(n-4)! = 132( n! /(n-2)!)

$\frac{(n-2)!}{(n-4)!} = 132 \\ \\ \frac{(n - 2)(n - 3)(n-4)!}{(n-4)!} = 132 \\ \\ (n - 2)(n - 3) = 132 \\ {n}^{2} - 5n + 6 = 132 \\ {n}^{2} - 5n - 126 = 0 \\ {n}^{2} - 14n + 9n - 126 = 0 \\ (n - 14)(n + 9) = 0 \\ since \: \: n \: \: is \: \: positive \: \: integer \\ n = 14$