This is a probability problem involving the outcomes of rolling three dice. Here's a breakdown of the task:

Task Overview:

You are asked to calculate the probabilities of the following events based on the outcomes of rolling 3 dice:

1. Event A: The sum of the dice is equal to $n$.
2. Event B: The product of the dice is equal to $k$.
3. Event C: The product of the dice is equal to $k$, given that the sum of the dice is equal to $n$.

The values of $n$ and $k$ are to be taken from the table, which lists different values for each option (numbered from 1 to 20). For each variant, the corresponding values of $n$ and $k$ are provided.

Table Interpretation:

• The first row in the table lists the variant number (1 through 20).
• The second row gives the corresponding value of $n$ for each variant.
• The third row provides the value of $k$ for each variant.

Next Steps:

Please select a variant number (from 1 to 20) for which you want to calculate these probabilities. Based on the chosen variant, I can proceed with specific calculations for the probabilities of the events $A$, $B$, and $C$.

Let me know which variant you would like to explore!