There is 5 players with 5 dices each = 25 throws per game Whats the probability that there is X dices with the value Y(1-6) on the table. for example. probability for 8 three's this is calculated through the binomial theorem right? http://en.wikipedia.org/wiki/Binomial_theorem where n=25, k=8 och p=1/6 calculating the probability of having X dices with the same value could be calculated with the above times six right? so far so good. now it gets a bit more complicated. how to calculate: how many dices of the same value is the most probable result? (assuming all 25 dices has been thrown) Also, conditional probability: i know that i have got Z dices with the same value (1-6 it doesnt matter which value). What is now the most probable result of the number of dices with the same value on the table?(i know my own result, but i dont know the 4 other players result) for instance: i get 4 three's. what is the most likely number of three's on the table totally of the 25dices? please refer to probability theory and distributions if you know them.