In the US, lotteries are a big business, raising huge revenues for state governments. But recently, here has been a controversy over the Texas state lottery.
There are various versions of the lottery but the one that gives out the biggest prize is where you pick six numbers from 1 through 54, with no number being repeated. If the drawing throws up that particular combination, then you win. The odds of winning are easy to calculate. The number of permutations of six numbers with none repeated is 18,595,558,800 (=54x53x52x51x50x49). Since the order of the numbers does not matter, there are 720 combinations that are equivalent (=6x5x4x3x2x1). Hence the number of possible results is the first number divided by the second, which gives 25,827,165. Since it costs $1 to pick a set of six, in theory if you buy one ticket for every possible combination, thus spending $25,827,165, you are guaranteed to win.
The catch is that the prize is usually less than that amount. A second problem is that if more than one person picks the same combination, then the prize gets split between the winners. A third problem is the sheer logistics of buying so many tickets, because the tickets are printed out by machines at various locations like convenience stores.
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