The prime factorisation of binomial coefficients

The binomial coefficient ¹⁰C₃ = 120. 120 = 2³ × 3 × 5 = 2 × 2 × 2 × 3 × 5, and 2 + 2 + 2 + 3 + 5 = 14. So the sum of the terms in the prime factorisation of ¹⁰C₃ is 14.

Find the sum of the terms in the prime factorisation of ^20000000C_15000000.

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