after rolling 5 dice , what is the probability that all 5 of the values are different?

720/7776

To calculate the probability of all five dice showing different values after rolling them, we need to count the number of outcomes where all five values are different and divide it by the total number of possible outcomes.

First, let's find the total number of possible outcomes when rolling five dice. Each die can have one of six possible values (1, 2, 3, 4, 5, or 6). Since we are rolling five dice, the total number of possible outcomes is 6^5 = 7776.

Next, we need to count the number of outcomes where all five values are different. For the first die, there are six possible values to choose from. After rolling the first die, for the second die, we have five remaining values to choose from. Similarly, for the third die, we have four values left, and so on.

So the number of outcomes where all five values are different is 6 * 5 * 4 * 3 * 2 = 720.

Finally, we calculate the probability by dividing the number of successful outcomes (720) by the total number of possible outcomes (7776).

Probability = Successful outcomes / Total outcomes
= 720 / 7776
= 0.0926

Therefore, the probability that all five dice show different values after rolling them is approximately 0.0926 or 9.26%.