Question

If nCn-4 = 15 , find n

Answer 1

My dear friend .......
nC(n-4)=15
n!/4!(n-4)!=15
n(n-1)(n-2)(n-3)/24 = 15
n(n-1)(n-2)(n-3)=360
6•5•4•3•2 = 360
Then n = 6

Answer 2

Given,

The value of nCn-4 = 15.

To Find,

The value of n.

Solution,

The formula for calculating the value of nCr is

nCr = n!/(n-r)!r!

In this case the value of r = (n-4).

So,

nCn-4 = 15

n!/(n-(n-4))!(n-4)! = 15

n!/(n-4)! = 15*4!

n(n-1)(n-2)(n-3) = 15*24

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

Comparing this equation with 6*5*4*3 = 360

So, n = 6

Hence, the value of n = 6.