Factorials are the way to go.
The MegaMillions lottery requires a customer to choose any five distinct numbers
between 1 and 56 as well as a single number between 1 and 46.
This means that for the first number, you have 56 choices. For the second number, you have
55 choices (you can re-use your number), for the third, 54 choices, etc. We can write this as
The last number doesn't
depend on the others; there are 46 possible choices for it. So we can just multiply by 46 to take
care of that.
Now remember that the last number (the one selected from 1-46) is identified separately from
the others, but the first five are just a group of numbers where order doesn't matter. So we need
to divide our answer so far by the number of ways you can re-organize the same 5 numbers. That's
also a factorial: 5!
When we put all this together, we get the final answer for the odds of winning the jackpot:
If you do the calculation correctly, you'll get the same odds that
Stephen La Rocque.