What is the probability that the sum of the three numbers is 11 if 3 dices are thrown simultaneously?

To calculate the probability that the sum of the three numbers on the dice is 11 when three dice are thrown simultaneously, we can break the problem into two parts:

1. **Total possible outcomes:**
   Each die has 6 faces, so when three dice are thrown, the total number of possible outcomes is:
   \[
   6 \times 6 \times 6 = 216
   \]

2. **Favorable outcomes:**
   We need to count how many combinations of three numbers from the dice sum up to 11. The three numbers on the dice range from 1 to 6, so we are looking for combinations of three integers \(x_1, x_2, x_3\) such that:
   \[
   1 \leq x_1, x_2, x_3 \leq 6 \quad \text{and} \quad x_1 + x_2 + x_3 = 11
   \]
   Let's systematically count the number of favorable outcomes by listing all possible triples:

   - (6, 4, 1)
   - (6, 3, 2)
   - (6, 2, 3)
   - (6, 1, 4)
   - (5, 5, 1)
   - (5, 4, 2)
   - (5, 3, 3)
   - (5, 2, 4)
   - (4, 4, 3)
   - (4, 3, 4)
   - (4, 5, 2)

There are likely several triples that can give

Discover the probability of rolling a sum of 11 with three dice. This problem covers probability theory and combinatorics, breaking down the total possible outcomes and favorable outcomes for a sum of 11. Suitable for students in Grades 6-8.

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