Question

C(n,2)=21 with solutions

Answer 1

Answer:

n is 7 see pic for explation please mark as brianlist I work hard for you

Answer 2

The combination is defined by,

$\rm{C(n,k)=\dfrac{n!}{k!(n-k)!}}$

Hence,

$\rm{C(n,2)=\dfrac{n!}{2!(n-2)!}}$

$\rm{C(n,2)=\dfrac{n!}{(n-2)!}}\cdot\dfrac{1}{2!}$

$\rm{C(n,2)=\dfrac{n(n-1)}{2!}$

Given that,

$\rm{C(n,2)=21}$

$\rm{\dfrac{n(n-1)}{2}=21}$

$\rm{n(n-1)-42=0}$

$\rm{n^{2}-n-42=0}$

$\rm{(n-7)(n+6)=0}$

$\rm{n=7\ or\ n=-6}$

But, $(-6)!$ is not defined.

$\rm{\therefore n=7}$