Balls, Balls, and Balls!

There are 1010 red \mathrm{\color{#D61F06}{red}} balls, 1010 blue \mathrm{\color{#3D99F6}{blue}} balls, and 1010 green \mathrm{\color{#20A900}{green}} balls.

How many different ways can you pick 1616 balls such that there is at least one ball for each color?

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