Egg Coloring

Yan Yau wants to paint eggs for Easter. He has 20 eggs and three colors, red green and blue. He wants the number of red eggs to be a multiple of three, green eggs to be a multiple of 4, and blue eggs to be a multiple of 5. If the number of eggs total that he paints is a multiple of 4, how many way can he paint eggs?

Details and Assumptions

Note that he can choose not to paint some eggs.

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