Mathematics, 22.11.2019 23:31 38saferguson

Give a combinatorial proof that $\underset{k=1}{\overset{n}{\su m}} k\binom{n}k^2 = n\binom{2n-1}{n-1}$ . [hint: count in two ways the number of ways to select a committee, with n members from a group of n mathematics professors and n computer science professors, such that the chairperson of the committee is a mathematics professor.]

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Give a combinatorial proof that [tex]\underset{k=1}{\overset{n}{\su m}} k\binom{n}k^2 = n\binom{2n-1...

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Give a combinatorial proof that . [hint: count in two ways the number of ways to select a committee, with n members from a group of n mathematics professors and n computer science professors, such that the chairperson of the committee is a mathematics professor.]

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