Lotto

49 balls, six places.

The formula says: n!/(k!(n-k)!) where n is the number of balls and k is the number of places. The explanation goes something like this:

There's 49 balls, there's 49 different options to choose from, so the chances are 1 in 49 of choosing the right one. Now, once we've chosen the first one we have 48 balls left, 48 different options to choose from. This combined to the first one yields 49*48=2352 different possibilities. It follows that the chances of choosing 6 different balls amounts to 49*48*47*46*45*44, each time one less than the previous. This can also be expressed as

49*48*47*46*45*44*43*...*1
-------------------------------
43*42*41*40*39*38*37*...*1

The 43*...*1 on the top cancels out with their respective numbers on the bottom, leaving us with the simple 49*48*47*46*45*44. Now, that division above can be expressed in a much more compressed format as such

  49!
-------
(49-6)!

Quick reminder, the expression n! in maths means the number n multiplied by all the numbers preceding it (n*n-1*n-2*n-3*...*1)

So we have that the chances of someone picking out the 6 correct balls in order are exactly 10,068,347,520.

Notice I said in order, but most lotteries don't follow order, they only ask you to match the numbers, in whatever order. So there's six balls to be picked, which means there's 6*5*4*3*2*1=720 different ways of ordering six balls. This can also be expressed as 6!, and the completed formula is thus:

   49!
---------
6!(49-6)!

This adds up to the slightly less impressive number of 13,983,816.

1 out of 13,983,816, that's the chance that you'll ever win the jackpot. Let me put it like this: 0.000000072.

The Lotto gets played every week, 13,983,816 / 52 = 268,919.5. That's how many years you'd have to play every week to be statistically guaranteed a jackpot. Even then, statistics guarantee nothing. Here's a good article, Big Brother's Guide To The Lottery, that goes into a bit more depth on what your chances are at the lottery, including a quote from 1984.

I was lying in bed thinking about the lottery and I got up specifically to write this piece. I read three issues of Transmetropolitan before going to bed, it seems to get me in a strange mood, I highly recommend reading this great comic, chapter one is free for download on PDF.