I play a game in which I have to throw a fair die repeatedly until I have thrown three sixes, after which I stop and note the total number of throws. What is the probability that I take six throws?
I did $(1/6)^3 \times (5/6)^3$ and this gave me $0.00268$ to 3.s.f.
This doesn't seem right as couldn't this be achieved in many ways by throwing the die to be 6 in different orders? E.g. $6,6,6$, non six,non six, non six OR 6,non six, non six, 6, 6, non six
Could anyone explain this?