Hi Harvey.
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 reuse your number), for the third, 54 choices, etc. We can write this as
a factorial:
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 146) 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 reorganize 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
MegaMillions reports.
Stephen La Rocque.
