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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!

Find the probabilities of the following events when rolling 3 dice: A - the sum of the dice is equal to n; B - the product of the dice is equal to k; C - the product is k, given that the sum is n. Values for n and k are provided in the table for 20 variants.

Explore the probability of specific events when rolling 3 dice, including calculating the probability of a sum n, product k, and conditional probability for these outcomes. This problem uses key probability theory concepts and is suitable for students in Grades 10-12.

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