Terms in a multinomial expansion

After combining like terms, how many distinct terms appear in the expansion of $(x_1 + x_2 + x_3 + x_4 + x_5 + x_6)^{18}$ ?

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A term is an exponent tuple $(e_1,\dots,e_6)$ with $\sum e_i = 18$ , $e_i\ge0$ .
Stars and bars: $\binom{18+5}{5}=\binom{23}{5}$ .

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