21. Argue that there are exactly $$binom{r}{k} binom{n-1}{n-r+k}$$ solutions of $$x_1 + x_2 + ... + x_r

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21. Argue that there are exactly

$$\binom{r}{k} \binom{n-1}{n-r+k}$$

solutions of

$$x_1 + x_2 + ... + x_r = n$$

for which exactly k of the xi are equal to 0.

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