Question

In a certain​ lottery, you must correctly select 44 numbers​ (in any​ order) out of 3939 to win. You purchase one lottery ticket. What is the probability that you will​ win?

Answer 1

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:

$\prod_{n=0}^{43} \frac{44-n}{3939-n} \approx 2.149332 \cdot10^{-104}$.

If you're wondering why i'm subtracting it's because each time you choose a number the # of choices decreases.