6. Give a combinatorial proof that the identity below for falling factorials holds for all x, y € R. -Σ(*) k [(x + y) (n) = Σ (k)y(n-k)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
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Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 16E
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6. Give a combinatorial proof that the identity below for falling factorials holds for all x, y € R.
-Σ(*)
k
((x+y)(n) =
(k)(n-k)
Transcribed Image Text:6. Give a combinatorial proof that the identity below for falling factorials holds for all x, y € R. -Σ(*) k ((x+y)(n) = (k)(n-k)
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Thanks but I need a combinatorial proof not a proof by induction

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