Prime Factorisation of Binomial Coefficients

The binomial coefficient $(\binom{10}{3}) = 120$ .
$120 = 2^{3} \times 3 \times 5 = 2 \times 2 \times 2 \times 3 \times 5$ , and $2 + 2 + 2 + 3 + 5 = 14$ .
So the sum of the terms in the prime factorisation of $(\binom{10}{3})$ is $14$ .

Find the sum of the terms in the prime factorisation of $(\binom{20 000 000}{15 000 000})$ .

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