Question

Show that

(

)

(

)

(

)

1,

,

1

,

CnkCnkCnk

+ =

− +

.

Answer 1

Show that $C(n,k)=C(n,n-k)$ :

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