SOLUTION: Prove that nC r + nCr-1 = n+1Cr

Question 666531: Prove that nC r + nCr-1 = n+1Cr
Answer by sachi(548) (Show Source): You can put this solution on YOUR website!
nCr+nCr-1=n+1Cr
or LHS=n!/[r!(n-r)!]+n!/[(r-1)!(n-r+1)!]
=n!/[r(r-1)!(n-r)!]+ n!/[(r-1)!(n-r+1)(n-r)!]
=n!/[(r-1)!(n-r)!]{[1/r]+[1/(n-r+1)]}
=n!/[(r-1)!(n-r)!]{(n+1)/r(n-r+1)}
=(n+1)n!/[r(r-1)!(n-r+1)(n-r)!]
=(n+1)!/[r!(n-r+1)!]
=n+1Cr
ans
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