Given the identity

$\displaystyle \sum_{i=0}^{n} \binom{k-1+i}{k-1} = \binom{n+k}{k}$

Need to give a combinatorial proof by interpreting the parts in terms of compositions of integers

(neither by induction nor using subsets)

:)

Please, help!

- Mar 19th 2013, 03:23 PMvercammenProve by interpreting the parts in terms of compositions of integers. Combinatorics.
Given the identity

$\displaystyle \sum_{i=0}^{n} \binom{k-1+i}{k-1} = \binom{n+k}{k}$

Need to give a combinatorial proof by interpreting the parts in terms of compositions of integers

(neither by induction nor using subsets)

:)

Please, help!