I think it is a simple question, but I do not get it.
If six-sided two dice are rolled and we are asked to find the probability of numbers summing up to 4, then number of outcomes we look for is 3, and they are:
(1,3), (2,2), (3,1)
Number of all outcomes is clearly 36.
The question is: Why we do not count the outcome (2,2) twice? It has two chances because it is possible to have number 2 on the 1st dice and 2 on the 2nd one, and vice versa, in the very same manner we count 3 and 1 twice.
To put the question in another form: Why arrangement is considered with different numbers while it is not with similar numbers?
Thanks in advance.