Number of possible combinations with a descending-value constraint

Question

I'm trying to solve an engineering problem regarding the optimization of electrical steel widths to compose a transformer core. At the end, I want to know how many combination can be made with based on two parameters: The number of steps in the core ($N$) and the number of available widths ($W$).

The constraint are:

• $W>N$
• widths need to be descending order.

As an example, the following table contains the solution for $W=4$:

N	W	Combinations	Number of combinations $C$
1	4	4 / 3 / 2 / 1	4
2	4	4-3 / 4-2 / 4-1 / 3-2 / 3-1 / 2-1	6
3	4	4-3-2 / 4-3-1 / 4-2-1 / 3-2-1	4
4	4	4-3-2-1	1

What I want is to find a function (with $W$ and $N$ as input) that gives me the $NC$. I couldn't find it so far.

Answer 1

Based on the comment done by @Daniel Mathis, it's clear that the problem is equivalent to the Binomial Coefficient. So, it could be solved by the following formula: $$C=\frac{W!}{N!(W-N)!}$$ using the $N$ and $W$ as presented in the question.