I'm currently studying diffusion theory and I'm hung up on a basic principle. Imagine a line that extends infinitely in either direction and in the middle is the origin. Where I'm hung up is here: say you had n moves and you wanted to know the number of paths to get to a point m units to the right of the origin and you could go left a times and right b times in one unit steps. My text gives this formula:
My problem is not that I don't know how to use this formula; instead, I don't understand how they arrived at this formula. Why do they use n! and why do they divide it by a!b!? Any insight into this would be appreciated.