Hey there community, I have a question on an exercise. Actually it is a general question based on it. Here is the exercise: We throw 3 dice. If we know that the sum of these 3 is 10, then what is the probability of at least one of them being 3? Well now, this exercise is very simple. I mean I can always find all the couples such as( 1,5,4),(5,4,1)... then I can find which of these couples contain at least one "3" and then we are done. But for an unknown reason, I don't " like" this solution. I mean, is this really the clever way? How about if I had 1000 dice and i knew that the sum of those were 3864 for example, would I have to count all the couples to answer this? So my question is, is there a possible way to answer this without having to count each and every couple that are out there? Because if there is, it would be nice to start figuring this out, with your help of course(if needed). Anyway, that's all. Thanks in advance for your time!