Question

if C(n,10)=C(n,12),determine n and hence C(n,5)​

Answer 1

Answer:

The value of n is 22

C(n,5)=26334

Step-by-step explanation:

Concept:

If C(n,x)=C(n,y) then n=x+y

$C(n,r)=\frac{n!}{(n-r)!\,r!}$

Given:

$C(n,10)=C(n,12)$

This implies,

$\implies\,n=10+12$

$\boxed{n=22}$

Now,

$C(n,5)$

$=C(22,5)$

$=\frac{22!}{(22-5)!\,5!}$

$=\frac{22!}{17!\,5!}$

$=\frac{17!*18*19*20*21*22}{17!\,5!}$

$=\frac{18*19*20*21*22}{5!}$

$=\frac{18*19*20*21*22}{1*2*3*4*5}$

$=\frac{3*19*21*22}{1}$

$=57*462$

$=26334$

Answer 2

hey come to the point