The same numbers twice...
Today's news carries this story from Bulgaria. The Bulgarian national lottery numbers were the same for two weeks in a row. This is attracting gasps of amazement from commentators and an investigation from the Bulgarian Lottery regulator. But the fact that this happened is actually not that surprising. The following explains why. Firstly, the paper is referring to these "identical" draws. They weren't. The numbers came out in a different order each time. For those who remember their high-school maths, this is the difference between a "permutation" and a "combination". The odds of 6 balls coming out in exactly the same order twice are very long, but with lotteries, you need the right numbers, you don't care in what order the balls emerge. This means we use the maths of combinations. The odds of winning first prize in the lottery are easily calculated. Lets say you are picking p balls from n possible numbers. The chance that the first ball out...