# Problem 231: The prime factorisation of binomial coefficients

![graphic](img231.gif)

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 20000000C15000000.