Combinatorics Problem

qwertychick

New member
Joined
Dec 16, 2020
Messages
1
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) ].

Please help
 

Jomo

Elite Member
Joined
Dec 30, 2014
Messages
11,483
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
Joined
Jan 29, 2005
Messages
11,391
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) ].

Please help
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
Joined
Oct 30, 2021
Messages
580
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.
 
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