Partition of a number

Let us define the number $n!$ as follows: n! = 1 \cdot 2 \cdot \ldots \cdot n if n > 0, and n! = 1 if n = 0. Let C(n, k) = \frac{n!}{k!(n - k)!} if 0 \leq k \leq n, and C(n, k) = 0 if k > n.

This number equals the number of combinations of $n$ elements taken $k$ at a time. In mathematics, such numbers are called binomial coefficients.

You are to represent the given number $P$ as the sum of three binomial coefficients:

where 0 \leq a < b < c.