Combinatorial Identity

Pietjuh

Can someone help me how to deal with this identity that i must prove?

$${n + k-1 \choose n - 1} = \sum_{i=1}^k {k-1\choose i -1} {n \choose i}$$

I've tried to figure out what the combinatorial meaning of the right hand side is, but I didn't succeed :(

Related Introductory Physics Homework News on Phys.org

PhilG

I think it will help to rewrite it in the form:

$${n + k-1 \choose k} = \sum_{i=1}^k {k-1\choose k - i} {n \choose i}$$

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving