Menu Close

show-that-C-n-1-n-r-1-C-r-n-r-1-

Tinku Tara 0 Comments
Pin




Question Number 34878 by NECx last updated on 12/May/18
show that C_(n−1) ^(n+r−1) =C_r ^(n+r−1)
showthatCn+r−1n−1=Cn+r−1r
Answered by Rasheed.Sindhi last updated on 12/May/18
^n C_r =((n!)/(r!(n−r)!)) C_(n−1) ^(n+r−1) =C_r ^(n+r−1) LHS:(((n+r−1)!)/((n−1)!(n+r−1− n−1 ^(−) )!)) (((n+r−1)!)/((n−1)!(n+r−1− n+1 )!)) (((n+r−1)!)/(r!(n−1)! )) RHS:(((n+r−1)!)/(r!(n+r−1−r)!)) (((n+r−1)!)/(r!(n−1)!)) LHS=RHS Proved
nCr=n!r!(n−r)!Cn+r−1n−1=Cn+r−1rLHS:(n+r−1)!(n−1)!(n+r−1−n−1―)!(n+r−1)!(n−1)!(n+r−1−n+1)!(n+r−1)!r!(n−1)!RHS:(n+r−1)!r!(n+r−1−r)!(n+r−1)!r!(n−1)!LHS=RHSProved

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *