Question

If nP4=20(nP2) find the value of n

Answer 1

hope it helps........

Answer 2

Answer: n = 7

Step-by-step explanation:

Since,

$^nP_r = \frac{n!}{(n-r)!}$

Here,

$^nP_4=20 ^nP_2$

$\implies \frac{n!}{(n-4)!}=20 \frac{n!}{(n-2)!}$

$\implies (n-2)! = 20(n-4)!$

$\implies (n-2)(n-3)(n-4)! = 20(n-4)!$

$\implies (n-2)(n-3) = 20$

$\implies n^2 - 5n + 6 = 20$

$\implies n^2 - 5n - 14=0$

$\implies n^2 - 7n + 2n - 14 = 0$

$\implies n(n-7)+2(n-7)=0$

$\implies (n+2)(n-7)=0$

If n+2 = 0 ⇒ n = -2 ( Not possible )

If n-7 = 0 ⇒ n = 7

Thus, the value of n is 7.