The prime factorisation of binomial coefficients

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

Find the sum of the terms in the prime factorisation of $20000000\choose 15000000$.