The number of ways of selecting $10$ balls out of an unlimited number of white, red, blue, and green balls is

This problem uses the stars and bars method for choosing r identical selections from n distinct categories, which follows the formula (n+r-1)C(r-1). Here, we select 10 balls from 4 colors, so n is 4 and r is 10. Substituting these values gives (4+10-1)C(10) which equals 13C10. By the symmetry property of combinations, 13C10 is equal to 13C3. The result is 13C3.

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