Zero!

The expression can be rewritten as: $\frac{50!}{24!}$ , where $!$ denotes factorial.

Since zero is just a power of 10, we can count fives (in this expression there are more twos than fives).

Counting zeros of $50!$ we have: $\left\lfloor\frac{50}{5}\right\rfloor + \left\lfloor\frac{50}{25}\right\rfloor = 10 + 2 = 12$ .

Counting zeros of $24!$ we have: $\left\lfloor\frac{24}{5}\right\rfloor = 4$

The fraction can be rewritten again as $\frac{a \cdot 10^{12}}{b \cdot 10^4} = \frac{a \cdot 10^{8}}{b}$ where $a$ and $b$ are some natural numbers (in other words - factorials without any powers of five and some powers of two).

Since $b$ divides $a$ , the number of zeros is $\boxed{8}$ .