One of my favorite quotes: "Lottery (noun) an extra tax for people who are bad at math." The record high Italian lotto prize is all over the news now. All you need to do, is pick the correct 6 numbers (out of 90). To educate the math-challenged I try to put the odds in perspective by telling them they can just as well pick the numbers 1,2,3,4,5 and 6. What are the odds that you randomly pick 1 through 6 out of 90 numbers? A quick calculation gives the odds of 1 in 623M. (6/90)*(5/89)*(4/88)*(3/87)*(2/86)*(1/85).
So... you can just as well pick the numbers 1,2,3,4,5,6. Or... can you?
I thought a little more about this. Let's assume I chose to mark 1,2,3,4,5,6 on my lottery form. And then, by sheer luck, the draw is 1,2,3,4,5,6. Now, I'm pretty sure that if this ever happens, the director of the lottery will nullify the results, and redo the draw. The director will assume the procedure was flawed, a computer failed, or something like that. So even when choosing 1,2,3,4,5,6 should give you even odds with any other combination, it may not be wise to pick those numbers.