I found in many or nearly all examples or tutorials, when talking about calculating the possibility of rolling dice, e.g. possibility of getting triple 1 when rolling 3 6-faces dices, are calculating with permutation, i.e. answer is 1 / (no. of possible outcomes) = 1 / 6 x 6 x 6 = 1/216
I'm very confused for that: why everyone is treating it as permutation, while the order of dice does not matter / assuming that the dices are indistinguishable ?
If we treat them as "permutations", every case would have an equal probability. For example, $$\mathbb P(1,2,1)=\mathbb P(2,1,1)=\frac{1}{216}$$ If we treated the above two cases as the same case (i.e. treating both cases as getting one 2 and two 1s), then each case would have different probabilities, which leads to trouble in calculations. For example, $$\mathbb P(\text{getting one 2 and two 1s})\ne \mathbb P(\text{getting one 1, one 2, one 3})$$ while we have something like $$\mathbb P(1,2,1)=\mathbb P(2,1,1)=\mathbb P(1,2,3)=\mathbb P(3,2,1)=\frac{1}{216}$$