Question

nP4=360,find the value of n

Answer 1

nP4 = 360
n! / (n-4)! = 360
n (n-1)(n-2)(n-3)(n-4)! / (n-4)! = 360
n (n-1)(n-2)(n-3) = 360
factorise 360 so that 360 can be written in the form of 4 consecutive numbers.
360 = 6×5×4×3
n (n-1)(n-2)(n-3) = 6×5×4×3
compare both L.H.S and R.H.S
therefore, n = 6

Answer 2

Answer:

6

Step-by-step explanation:

Given : $^nP_4=360$

To Find: value of n

Solution:

Formula of permutation : $^nP_r=\frac{n!}{(n-r)!}$

Substitute r = 4

$^nP_4=\frac{n!}{(n-4)!}$

$^nP_4=\frac{n(n-1)(n-2)(n-3)(n-4)!}{(n-4)!}$

$^nP_4=n(n-1)(n-2)(n-3)$

Since we are given that $^nP_4=360$

So, $360=n(n-1)(n-2)(n-3)$

$360=n(n-1)(n-2)(n-3)$

Factorize 360

$6 \times 5 \times 4\times 3=n(n-1)(n-2)(n-3)$

On comparing n =6

Hence the value of n is 6