1. ## Dice

What is the probability of throwing exactly two 3x a two and 2x a three with five normal dice? Order is not to be respected (eg 22233=32322)
The possible combinations for n=6 and k=5, if order is to be neglected and repetition (as the task is about dice) is possible, is the formula (n+k-1 // k) which equals 720 possibilities. Thus the probability for axactly two threes and three twos is 1/720.
The solution is 10 //7776 though. Where is my mistake?

Thanks

If we throw a die five times there are $6^5$ different possible outcomes(5-tuples).
Of those there are only 10 that contain exact two 3's and three 2's.
So what is the probability?

3. But why do you have do consider order when 33322 is the same as 32223 - I still dont get that. 6^5 possibilities would be right if there was a difference between e.g 21 an 12...

4. Originally Posted by Schdero
I still dont get that. 6^5 possibilities would be right if there was a difference between e.g 21 an 12...
Once again: order must be considered.
The pair $(1,2)$ is different from the pair $(2,1)$.
If the question were, "what is the probability of tossing a one and a two?"
The answer is $\frac{2}{36}$ because there are two ways out of thirty-six to do it.

From a content point of view there are only 21 different outcomes.
But the difference is that all contents do not have the same probability.