Probability of rolling a dice 3 times

c). {1, 2, 3} in any order

for example in c, i get that it;s 3/6 x 2/6 x 1/6, since the first dice can be any of the of 3, but that means the 2nd dice can only be 2 of the remaining left, and then the last dice can only be 1 option.

f). {1, 1, 2} in any order

for f, would it be that i have to add up the probabilities of getting (1,1,2), (1,2,1) and (2,1,1) which gives me 3/216

There is no difference between these two questions. The probability of any given value falling in any given slot is the same 1/6 each, 3/216.

The notion of 3/6 x 2/6 x 1/6 is for dependent random variables only; aka sampling without replacement. Rolling one die does not change the possible outcomes available to the next roll.

/r/probabilitytheory Thread