Suppose a roulette (with 38 numbers) is spun 12 times, and the probability of any number repeated is required.
Working 1: 38C1*12C2*(1/38)^2*(37/38)^10.......gives a value greater than 1 so obviously wrong. (success occuring twice for a single number, then accounting for 38 separate no.s)
Working 2: No repeat= 38*37*36*..*27/(38)^12. So at least one repeat=1-no repeat=1-.143=.857 probability...looks better, and sufficient for my task.
Problem is...how do I find out the probability of any number occuring thrice exactly, or at least probability of any number occuring twice exactly, as the working 1 doesn't work, and working 2 is only applicable for the special case and no more Why just when I think I have learnt something about probability it eludes me.