Understanding Vandermonde's Identity: Explanation and Proof

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Vandermonde's Identity relates to combinatorial coefficients and is expressed as the sum of products of binomial coefficients. The identity states that the number of ways to choose k elements from a set of n + m elements can be represented as the sum of ways to choose j elements from n and k - j elements from m. The proof typically involves combinatorial arguments or generating functions. Participants in the discussion seek clarification on the proof's steps, indicating some confusion despite understanding related concepts like the Binomial theorem. The conversation highlights the need for clear explanations in mathematical discussions.
Chromium
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Hey guys,

Could someone give me a clear explanation of what Vandermonde's Identity is? I'm looking at the proof in my book and I'm having a difficult time understanding this. Fortunately I understand the rest of the section (which covers Binomial theorem, Pascal's identity and triangle).

thanks
 
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Could you be more specific as to what you don't get? The proof is rather straightforward.
 
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Off-Topic: Every time someone post's a thread on this topic, I keep wondering why people talk about Harry-Potter-stuff on the maths forums. :biggrin:
 

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