Lotto
49 balls, six places.
The formula says: n!/(k!(nk)!)
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!  (496)!
Quick reminder, the expression n! in maths means the number n multiplied by all the numbers preceding it (n*n1*n2*n3*...*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!(496)!
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.

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