If " "((n), (k))=((n!), (k!(n-k)!)) " " show that " "((n), (k))=((n), (n-k))...?

1 Answer
Feb 15, 2018

"See explanation"

Explanation:

"This is trivial."
((n), (k)) = ((n!),(k!(n-k)!))" (definition combination)"
=> color(red)(((n), (n-k))) = ((n!),((n-k)!(n-(n-k))!))
= ((n!),((n-k)!k!))" (n-(n-k) = n-n+k = 0+k = k)"
= ((n!),(k!(n-k)!))" (commutativity of multiplication)"
= color(red)(((n),(k)))" (definition combination)"