Choice of throwing 12 in a single throw with three dice

To find the probability of throwing a sum of 12 with three dice in a single throw, we need to determine the number of favorable outcomes and the total number of possible outcomes.

Favorable outcomes:
To get a sum of 12, we can have the following combinations of numbers on the three dice:

- 6 on the first die, 6 on the second die, and 0 on the third die
- 6 on the first die, 5 on the second die, and 1 on the third die
- 6 on the first die, 4 on the second die, and 2 on the third die
- 6 on the first die, 3 on the second die, and 3 on the third die
- 5 on the first die, 5 on the second die, and 2 on the third die
- 5 on the first die, 4 on the second die, and 3 on the third die
- 4 on the first die, 4 on the second die, and 4 on the third die

So, there are a total of 7 favorable outcomes.

Total number of possible outcomes:
When three dice are thrown simultaneously, each die can have 6 possible outcomes (numbers 1 to 6). Since there are three dice, the total number of possible outcomes is 6 x 6 x 6 = 216.

Probability:
The probability of an event is given by the ratio of favorable outcomes to total outcomes.

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

In this case, the probability of throwing a sum of 12 with three dice is:

Probability = 7 / 216

Therefore, the correct answer is option D, 25/216.