I calculated the propabilites to get numbers 2 to 12 by throwing 3 dices and picken only 2 out of them.
If someone throws 3 times a 1 the event is [1, 1, 1]. There are 3 possible combinations to get a 2 out of the thrown dice.
I summarized all possible combinations for 2, 3, 4, 5, ..., 12. Eachs has his own sum. At the end i divided each counter by the sum of all counted combinations.
For throwing a 2 there exist in total 18 combination. If I divide 18 by the sum of all counted possible combinations, the propability is the same as I just throw 2 dices.
The results for 2 up to 12 are all equal. So apparently it does not matter if you throw 3 dices and pick 2 of them or just throw 2 dices. But it feels kinda wrong to me that they seam to be the same.
Am I doing a mistake or are the propabilites the same for throwing 2 dices and throwing 3 dices but pick 2 out of them?
Hopefully you can understand my explanation, I am no native speaker.