Question

Find n if ;12×n-1p3=5×n-1p3

Answer 1

The value of n is "8".

Step-by-step explanation:

We have,

12 × P (n - 1, 3) = 5 × P (n + 1, 3)

P (n - 1, 3): P(n + 1, 3) = 5 : 12

⇒$\dfrac{(n-1)!}{(n-4)!} : [tex]\frac{(n + 1)!}{(n -2)!}$ = 5 : 12

⇒ $\dfrac{(n-1)!}{(n-4)!} \times [tex]\frac{(n - 2)!}{(n + 1)!}$ = $\frac{5}{12}$

⇒ $\frac{(n -2)(n - 3)}{n(n + 1)}$  = $\frac{5}{12}$

⇒ 7·$n^{2}$ - 65·n + 72 = 0

⇒ 7·$n^{2}$ - 56·n - 9·n + 72 = 0

⇒ (n - 8)(7n - 9) =0

∴ n = 8 [∵ n is never fraction)

Hence, n = 8.

Answer 2

Step-by-step explanation:

here is your answer the answer is 8