Calculating the probability of rolling 3 different numbers on 3 dice:

To calculate the probability of rolling 3 different numbers on 3 dice, we need to first determine the total number of possible outcomes when rolling 3 dice.

Determining the total number of possible outcomes:

When rolling 3 dice, each die can land on one of 6 possible numbers. Therefore, the total number of possible outcomes is:

6 x 6 x 6 = 216

Determining the number of outcomes where all 3 numbers are different:

To determine the number of outcomes where all 3 numbers are different, we can use the following formula:

n! / (n-r)!

Where n is the total number of possible outcomes (216) and r is the number of dice being rolled (3).

Using this formula, we get:

6! / (6-3)! = 6 x 5 x 4 = 120

Therefore, there are 120 possible outcomes where all 3 numbers are different.

Calculating the probability:

To calculate the probability of rolling 3 different numbers on 3 dice, we simply divide the number of outcomes where all 3 numbers are different by the total number of possible outcomes:

120 / 216 = 5/9

Therefore, the probability of rolling 3 different numbers on 3 dice is approximately 0.556 or 55.6%.