How many lottery tickets do you need to buy to guarantee getting five numbers?

If, as you say, you're not concerned about the 6th ball:





On the first ball, there are 49 total balls, and 5 of them are the in the winning combination.





On the second, there are 48 balls, 4 winners.





Etc.


...





(49/5) * (48/4) * (47/3) * (46/2) * (45/1) = 1,906,884 possible cominbations





You would need 1,906,884 tickets.How many lottery tickets do you need to buy to guarantee getting five numbers?
There are 49C6 possible combinations of numbers which is 13983186. Of these, 6C5 times 43C1 which is 258 have (exactly) 5 of the correct numbers. If you were highly unlucky, you could buy the other 13983558 tickets first before you got one with 5 numbers. So you'd have to buy 13983559 to be guaranteed to have five digits. (Subtract one if you meant at least 5, because one of the combinations will have all 6 numbers.)How many lottery tickets do you need to buy to guarantee getting five numbers?
all of them
dont know...but I've heard of people spending their savings on the big ones. Right now we have $117,000,000 for tonight.
Basically you need to look at it this way. You have 49 balls in the lottery.


So the first ball that comes out in the draw will have 49 possible values, then the second which is drawn will have 48 possible values (as you can't have the same number twice) and so on.


So there will be 49*48*47*46*45*44 choices. However this assumes that the order matters, but the order in which they come doesn't matter for the lottery, so divide by 6!to get rid of this redundancy.


So there are 13983816 possible combinations for the lottery and you would need to buy that many tickets.
pablodiablo1981 is correct. You would have to buy 1,906,884 tickets in order to guarantee matching five numbers in a 6/49 game.





Unfortunately, I don't think there is any 6/49 lotto in the world that pays enough for a five out of six match to make that kind of expenditure profitable. The lower secondary prizes which you would also win in the process would help to lessen the loss, but you'd still come out a loser.





All lottery games have a huge house percentage which is nearly impossible to overcome unless you're lucky enough to win a jackpot. You can get ahead at any prize level with luck, but you can't beat them by buying such a huge number of tickets unless you wait until the jackpot amount is up to an overlay level where the size of the jackpot is greater than the odds of winning it. If you buy all the possible combinations when the jackpot is at such a level, you will in theory beat the odds. Of course, if there are others who hit the jackpot at the same time, they will most likely diminish your winnings to the level of a loss. Also, you must consider taxes will also be taken out, so that will also decrease your winnings.





In short, simply buying such a large quantity of tickets is not a good strategy for coming out ahead in playing the lottery.