Me and a friend of mine had into a little dispute about this issue, and I'd love if you guys could settle this.

The lottery in our country draws every weak 6 balls out of a pool of 37 balls (numbered 1,2,...37).

In each lottery ticket you need to guess 6 numbers.

For the sake of simplicity, let's assume that only a correct guess of 6 numbers will be considered as "winning the lottery" (even though in reality you'll also get a prize for guessing 5 or even 4 numbers).

The chance of winning the lottery, if you fill onlyoneticket, will then be 1 to 37x36x35x34x33x32. there's no argue here.

Now, he claims that any additional ticket I fill is going to improve my chances, so, if I will fill, say, n lottery tickets, my chances will then be n to 37x36x35x34x33x32 (adding 1/(37x36x35x34x33x32) n times).

I claim that this is not true, since this calculation ignores the fact that two (or more) tickets can have the same numbers in them.

For example, if I filled two tickets with exactly the same numbers, I didn't improve my chances whatsoever!

to this he replied "OK, so choosing different numbers in any ticket will give the above calculation..."

But then I thought about it a little and said that first of all, you can only produce 6differentlottery tickets (by the pigeonhole principle), so even if his observation is true, then for $\displaystyle n>6$ the chances will not be improved by as much as he said, and second, I'm not even sure that he's correct for n less then or equal to 6.

I know very little about probability and random variables, but is there a random variable (or a sequence of random variables) that describes the chance of winning the lottery with k lottery tickets? or is it to complex to determine?