To determine the number of possible outcomes in which at least one dice shows the number 2, we can use the principle of complementary counting.

First, let`s find the total number of possible outcomes when three dice are rolled. Each dice has six faces, so the total number of outcomes for rolling three dice is 6 x 6 x 6 = 216.

Next, let`s find the number of outcomes in which none of the dice show the number 2. Since there are three dice and each has five faces without the number 2, the number of outcomes where none of the dice show 2 is 5 x 5 x 5 = 125.

Finally, we can find the number of outcomes in which at least one dice shows the number 2 by subtracting the number of outcomes where none of the dice show 2 from the total number of outcomes:

Number of outcomes with at least one dice showing 2 = Total number of outcomes - Number of outcomes with none of the dice showing 2

= 216 - 125

= 91.

Therefore, the correct option is Option 3: 91.

We can also verify this result by considering the possible scenarios where at least one dice shows the number 2:

1. The first dice shows 2, and the other two dice can have any of the six numbers: 6 x 6 = 36 outcomes.

2. The second dice shows 2, and the first and third dice can have any of the six numbers: 6 x 6 = 36 outcomes.

3. The third dice shows 2, and the first and second dice can have any of the six numbers: 6 x 6 = 36 outcomes.

4. Both the first and second dice show 2, and the third dice can have any of the six numbers: 6 outcomes.

5. Both the first and third dice show 2, and the second dice can have any of the six numbers: 6 outcomes.

6. Both the second and third dice show 2, and the first dice can have any of the six numbers: 6 outcomes.

7. All three dice show 2: 1 outcome.

Adding up these possibilities gives us a total of 36 + 36 + 36 + 6 + 6 + 6 + 1 = 91 outcomes, supporting our previous calculation.