Prove the following.
rC(n,r) = nC(n-1,r-1)
I prove to
LHS = r((n!)/(n-r)!r!)
RHS = C(n-1,n-r) then do not know how to do.
M2 Factorial Notation
2011-03-17 2:45 am
回答 (1)
2011-03-17 2:57 am
✔ 最佳答案
RHS =n*C(n-1,n-r)
=n*(n-1)!/{[(n-1)!-(n-r)!](n-r)!}
=n*(n-1)!/[(r-1)!(n-r)!]
=n*[(n-1)!*nr]/{[(r-1)!(n-r)!]*nr}
=n!r/[r!(n-r)!]
收錄日期: 2021-04-22 00:53:06
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20110316000051KK00810