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Let 1 ≤ m ≤ n be integers. Give a combinatorial proof of the identity n+m Σ (:) ( ".) ( ^_) - (.") ("+"). 2 km) m) k=n-m Hint: Think of the number of ways of choosing a team of n players from given two groups of n people and choosing n-m of these players as team leaders with some additional restriction. You need to figure out what should this "additional restriction" be.

Let 1 ≤ m ≤ n be integers. Give a combinatorial proof of the identity n+m Σ (:) ( ".) ( ^_) - (.") ("+"). 2 km) m) k=n-m Hint: Think of the number of ways of choosing a team of n players from given two groups of n people and choosing n-m of these players as team leaders with some additional restriction. You need to figure out what should this "additional restriction" be.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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7. Let 1< m <n be integers. Give a combinatorial proof of the identity k n 'n + m = - m п — т. m k=n-m Hint: Think of the number of ways of choosing a team of n players from given two groups of n people and choosing n – m of these players as team leaders with some additional restriction. You need to figure out what should this "additional restriction" be.
Transcribed Image Text:7. Let 1< m <n be integers. Give a combinatorial proof of the identity k n 'n + m = - m п — т. m k=n-m Hint: Think of the number of ways of choosing a team of n players from given two groups of n people and choosing n – m of these players as team leaders with some additional restriction. You need to figure out what should this "additional restriction" be.
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