How many rain drops in a storm? According to Rain Wiki :

Heavy rain — when the precipitation rate is > 7.6 mm (0.30 in) per hour,[106] or between 10 mm (0.39 in) and 50 mm (2.0 in) per hour

According to USGS Water Science School :

We can call the growing droplet a raindrop as soon as it reaches the size of 0.5mm in diameter or bigger. If it gets any larger than 4 millimeters, however, it will usually split into two separate drops.

If its raining heavy, how many rain drops are there per square meter per hour?
 A: Well, $7.6\,\text{mm}/\text{h}$ is the same as $7.6\,\text{l}/\text{m}^2\text{h}$.
The volume of a raindrop with diameter in the range $0.5\ldots 4\,\text{mm}$ is $\frac43\pi r^3\approx 0.065\ldots 34\,\text{mm}^3$. Dividing $7.6\,\text{l}/\text{m}^2\text{h}=7.6\text{dm}^3/\text{m}^2\text{h}=7.6\cdot 10^6\,\text{mm}^3/\text{m}^2\text{h}$ by these volumes, gives us a count of 
$$\frac{7.6\cdot 10^6\,\text{mm}^3/\text{m}^2\text{h}}{34\,\text{mm}^3}\ldots \frac{7.6\cdot 10^6\,\text{mm}^3/\text{m}^2\text{h}}{0.065\,\text{mm}^3} \approx 2\cdot 10^5\ldots\, 10^8\;\text{m}^{-2}\text{h}^{-1}$$
As the $7.6\,\text{mm}$ were only a lower bound, we can say that there are at least 200,000 drops per square meter and hour in a heavy rain, but typically a lot more (as in, several millions).
I leave it to you to make the corresponding computations for $10\,\text{mm}$ and $50\,\text{mm}$ and thereby find a range of possible drop counts under the alternative definition of heavy rain.
Btw, I suppose one can safely assume that the majority of drops in  aheavy rain are mauchlarger than the lower end of the spectrum, but this cannot be inferred from the text quotes given.
