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Counting & ProbabilityEasyIdentities and Techniques, Proved

Identities and Techniques, Proved · Easy problem

A club has 5 boys and 4 girls. Adding up the counts of 3-person committees with 0, 1, 2 and 3 boys gives

(50)(43)+(51)(42)+(52)(41)+(53)(40).\binom{5}{0}\binom{4}{3}+\binom{5}{1}\binom{4}{2}+\binom{5}{2}\binom{4}{1}+\binom{5}{3}\binom{4}{0}.

Use Vandermonde's identity to find this sum.

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