Question

np6 =3×np5 find the value of n

Answer 1

I hope this helps!

@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@'

Answer 2

The value of n is 8.

Step-by-step explanation:

We have,

$^{n} P_6=3\times ^{n} P_5$

To find, the value of n = ?

∴$^{n} P_6=3\times ^{n} P_5$

$\dfrac{n!}{(n-6)!} =3\times \dfrac{n!}{(n-5)!}$

[ ∵ $^{n} P_r=\dfrac{n!}{(n-r)!}$]

⇒ $\dfrac{1}{(n-6)!} =3\times \dfrac{1}{(n-5)!}$

⇒ $\dfrac{1}{(n-6)!} =3\times \dfrac{1}{(n-5)(n-6)!}$

⇒ $1 =3\times \dfrac{1}{(n-5)}$

⇒ n - 5 = 3

⇒ n  = 3 + 5 = 8

Hence, the value of n is 8.