Why divide by 2 when finding probability of exactly 2 values on 5 dice

[rad0786]

Hello, I have two questions regarding probaility, i was hoping some body can help me out.
I know that this is a "Physics Forum" However, i thought somebody might still beable to help :)


When rolling 5 distinuishable dice, find the probability that there are two different values?

I did this by (6 x 5 x 4)/2 x ( 5 ) = 1800
(2 2 1)

and the probability is 1800/(6^5) = 0.23148

Now, I am wondering WHY do you divide the (6 x 5 x 4) by 2?

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[member 553083]

The reason why you divide the (6 x 5 x 4) by 2 is because you are counting each possible combination twice. For example, if you rolled a 1, 2, 3, 2, and 1, then you have two different values (1 and 2). However, this would be counted twice in your calculation since the ordering of the dice does not matter. Therefore, you must divide by two to avoid double-counting the same combination.