More Balls and Boxes (Sorta) : Inclusion and Exclusion Problem with Multichoosing - Combinatorics

How many ways are there to pick 30 balls from 10 red, 10 blue, 10 orange, and 10 yellow balls? The order you pick them in does NOT matter, and balls of the same color are indistinguishable. John runs through this problem using the principle of inclusion and exclusion with multichoosing.
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