Math Problem Statement

b. How many possible outcomes are there if you toss

threethree

66​-sided

​dice?

enter your response here

outcomes

​(Type a whole​ number.)

Solution

To find the number of possible outcomes when tossing three 6-sided dice, we need to calculate the total combinations that can occur with three dice, each having 6 faces.

Each die has 6 possible outcomes (1 through 6). Since the rolls are independent of each other, we multiply the outcomes of each die:

6×6×6=63=2166 \times 6 \times 6 = 6^3 = 216

Thus, there are 216 possible outcomes when tossing three 6-sided dice.

Would you like further details on this calculation, or have any questions?


  1. How many outcomes are there with four 6-sided dice?
  2. What is the probability of rolling three identical numbers with three 6-sided dice?
  3. How many possible outcomes are there with three 4-sided dice?
  4. What is the probability of rolling a sum of 10 with three 6-sided dice?
  5. How many possible outcomes are there if you roll three 8-sided dice?

Tip: When calculating possible outcomes with independent events, multiply the number of outcomes for each individual event.

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Probability

Formulas

Total outcomes = 6^3 = 216

Theorems

Multiplication Rule of Counting

Suitable Grade Level

Grades 7-9