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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.