# Combinatorics Problem

#### qwertychick

##### New member
Prove the cancellation identity for generalized binomial coefficients: if α is a real number, and k, m are nonnegative integers, then
(α C k)(k C m) = [α C m] [ (α − m) C (k − m) ].

#### Jomo

##### Elite Member
No one here can help you if you do not show any work!
Just use the definition nCr = n!/[r!(n-r)!] for both sides, simplify and the results will be equal.

#### pka

##### Elite Member
Prove the cancellation identity for generalized binomial coefficients: if α is a real number, and k, m are nonnegative integers, then
(α C k)(k C m) = [α C m] [ (α − m) C (k − m) ].

This appears to be an really ill-defined problem. It says that if [imath]\alpha\in\mathbb{R}~\&~\{k,n\}\subset\mathbb{N}^+[/imath] then....
But that would mean that [imath]^{\sqrt[3]{15}}\mathcal{C}_{5}[/imath] is defined. I don't recognize that a in any use of combinations.
Please review the post and either correct or explain what is meant.

#### blamocur

##### Full Member
This appears to be an really ill-defined problem. It says that if [imath]\alpha\in\mathbb{R}~\&~\{k,n\}\subset\mathbb{N}^+[/imath] then....
But that would mean that [imath]^{\sqrt[3]{15}}\mathcal{C}_{5}[/imath] is defined. I don't recognize that a in any use of combinations.
Please review the post and either correct or explain what is meant.

#### blamocur

##### Full Member
Forgot to mention that the link points to the generalized binomial coefficients, which can be defined even for complex [imath]\alpha[/imath]'s.