Reducing $\frac{B!(C-B)!}{A!(B-A)!}$ where $A \le B \lt C$

Question

I have three positive integers: $A \le B \lt C$

I want to reduce the expression $$\frac{B!(C-B)!}{A!(B-A)!}$$

This is always an integer, but I'm having trouble reducing out the fraction expression.