8. Prove that $$ binom{n+m}{r} = binom{n}{0}binom{m}{r} + binom{n}{1}binom{m}{r-1} + ... + binom{n}{r}binom{m}{0} $$ HINT: Consider a

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8. Prove that

$$

\binom{n+m}{r} = \binom{n}{0}\binom{m}{r} + \binom{n}{1}\binom{m}{r-1} + ... + \binom{n}{r}\binom{m}{0}

$$

HINT: Consider a group of n men and m women. How many groups of size r are possible?

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