The probability of choosing one correct number is 44/3939.
The prob. of choosing 2 s 44/3939 * 43/3938.
And so on...
In product notation it looks like this:
[tex]\prod_{n=0}^{43} \frac{44-n}{3939-n} \approx 2.149332 \cdot10^{-104}[/tex].
If you're wondering why i'm subtracting it's because each time you choose a number the # of choices decreases.