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)