The formula you gave seems incorrect to me. I know you said it's high school math, but I guess I forgot it.

It works, for the example, but I don't see how it could work for many other ones.

For example, say you have a 3x3 matrix. With your formula, it would be 3!/(3!*(3 - 3)!) = 1. It seems to me like there would be more than one way to make it down in a 3 by 3 matrix. In fact, matrix with the same number of rows and columns would equal 1 with the formula n! / r!(n-r)!.

Am I missing something here?