A probability of an event can be computed as the ratio between the amount of outcomes which are part of the event and the total outcomes in the sample space. (Given a sample space which has the same probability for each outcome).
But, in this approach, when outcomes are subsets of a set (as in rolling k dices), one needs to count outcomes by using permutations (not combinations).
How can I better explain this to students ? Most people are tempted to use combinations if nothing is said about order.
An example of the confusion (poorly answered, in my opinion): Different probabilities with permutation and combination?)
Some fragments of the answer here are my favorite so far, the relevant phrases are:
Imagine the dice as being tossed one at a time, or imagine them different-coloured
and
The big problem is that if we do not consider order, then not all outcomes are equally likely. For example, five 1's is substantially less likely than getting a pattern of 5 numbers that consists of the numbers 1, 2, 3, 4, and 5. Indeed, the latter is 120 times as likely as the former.
Thus if we use sequences as outcomes, or equivalently consider the dice to be of different colours, we get that all outcomes are equally likely, and we can obtain other probabilities by simply counting.