(no subject)

[cailj]

Okay, math geeks, I have a question.

You have a certain number of numbers, X. How many unique sets of Y numbers can be created out of X? i.e., how many unique combinations of 5 numbers can be made if you have 25 numbers?

Or, to put it in more interesting terms, if you have 40 numbers, how many tickets must you buy in order to guarantee a win of all 6 numbers in a lottery? I remember there was a formula for this when I was in stats, but I don't remember what it was.

Comments

[steam.livejournal.com]

okay, it's been a Long Time since I knew this well, but:

If there are N balls and you're picking P of them:

n!/p!(n-p)!

so:

40! / (6! * (40-6)!)

And I don't have a convenient way to do factorials here, so I leave it up to you to simplify.

I know for 49 ball lotto, it's about 14,000,000 combinations. so the odds are 1:14000000 for a single ticket to win.

[shadowblue.livejournal.com]

There are two different things, combinations and permutations, that you're probably thinking of.

The notation is nCk and nPk, where n is the set size and k is the number of items you want to get. My math teacher liked to call C 'choose', and P 'pick', but I don't know if that helps remember the difference, which is: permutations allow, for example, that AB and BA are two different results, where in combinations that would just be one result.

Anyway, for lotteries etc, you want combinations, and the person above me had the right formula for that. But for a second I thought it was wrong.. turns out all I did was type it in wrong.

According to this thing, there are 3,838,380 6-item combinations from a set of 40.

And 53,130 of 5-item combos from a set of 25.

Crazy math.