# After rolling four dice, what is the probability that all four dice show different numbers?

##### 1 Answer

#### Explanation:

Let

In order to find

If we keep going, assuming we keep rolling different numbers, then on roll three, there are 4 acceptable outcomes, and on roll four, there are 3 acceptable outcomes. (As the roll counter goes up, the number of possible unique rolls goes down.)

Assuming independence of rolls, we get

Since

#"P"(E)=360/6^4=60/216=5/18,#

which is approximately 27.78%.