Five die are tossed and the uppermost face on each die is observed. What is the probability that the uppermost faces of these five dice at least two of the uppermost faces show the same number?
I start by finding the total number of possibilities of rolling the five dice. which is 6*6*6*6*6 = 7776 total possibilities.
For the dice one of the dice has a probability of (6c1) , this is because it has 6 choices it can be but we want to choose one to set the other dice to be this number. The other dice that will have the same number has a probability of (1c1), because there is only 1 possibility for what it can be in order to match the other dice and we choose that possibility. The other three dice have 6 possibile options for what they can be.
Therefore the probability would be ((6c1)(1c1)(6)(6)(6)/(7776)) = 0.1666 or ~17%.