Number of possible lottery combinations

[Blackraven]

Hmm.....

I just had a thought recently with regards to the lottery (like the one we have here where I'm from) and that thought was this: How much can one person spend that would guarantee him/her into winning a lottery jackpot? In other words, what if he/she buys an bets for all possible combinations? As absurd and money-wasting as it is, well, at least it guarantees that he/she would always win the jackpot (either as a solo win or if the pot has to be shared with other winners).

In any case, I know that there is actually a way to compute for this process. Unfortunately though, I suck at 'math' (or 'maths' if you use the British system of English) and as thus, I've forgetten how to do it. I've read a few sites as to this and many of them all point to the concept and/or field of Combinatorial Mathematics (something that I took up both in High School years ago and in my Discrete Mathematics class last year though I forget everything about it). Stuff like set theory, cardinality and such......

In this regard, maybe you guys could help me out here with this one:

I am deciding to enter the lottery for a 6/42 draw. This basically involves a a 6-digit number and within each respective digit, one must choose a number between 1 to 42.

Sample:
01-18-27-42-08-23

Question: How many possible combinations would it take to satisfy all possible combinations in the 6/42 draw (such that you are guaranteed to win the jackpot prize either for yourself or as split pot between another winner or winners)???

Also: Same principle (a 6-digit game) but in each digit, one can only pick from the numbers 1 up to 9. How many possible variations? (I'm trying to do this manually by jotting down every possible entry )

That's basically it (so far).

P.S.
I forgot about my concepts but:
Why didn't we use 'permutation' instead? What is permutation? How exactly does it differ from combination? (the wiki article didn't seem so clear on it)

[deathrazor]

Permutation is finding the number of experimental outcomes when n objects are selected out of a set of N objects. The difference from combinations is that the order of selection makes a difference on the outcomes. In combinations it doesn't matter, so you use that for lottery examples. For your 6 set of 42, you would have to use (42!)/(6!(42-6)!) [! is factorial, look it up if you don't know it]. There are 5,245,786 possible combinations for your lottery, meaning you have a 1/5,245,786 chance of exactly matching the numbers.

(ps I'm in a business stats class right now, which is why I still know all of this)

pps arctures is wrong

[Arctures]

Originally Posted by deathrazor

pps arctures is wrong

yeah I just figured that out

[deathrazor]

oh for your 9 number set there are 84 possible combinations.

[Excel-2010]

I've been playing 5-7-3 in Virginia's Pick 3 for a while now. I'll donate some of it here when I do win.

[ranatalus]

the one fucking time i was in a gas station and did NOT decide to play 5-7-3 is the one fucking time it came up

also, the pick4 that day was 5-7-3-0 which was just god fucking mocking me

[Irob]

Originally Posted by ranvlm_zkatalus

the one fucking time i was in a gas station and did NOT decide to play 5-7-3 is the one fucking time it came up

also, the pick4 that day was 5-7-3-0 which was just god fucking mocking me

this is awesome.

[Heavy Metal Hero]

Basically though, in no lottery in the world is it possible to turn a guarenteed profit by buying every ticket. You're guarenteed to spend more (typically a lot more) than you will make back.