A eighteen-sided die is rolled three times. In how many ways can this happen?
How would I solve this problem?
any of 18 different numbers can show on each roll.
So, there are 18*18*18 different sets of 3 events
5832
To solve this problem, you can use the concept of the multiplication principle. The multiplication principle states that if there are m ways to do one thing and n ways to do another thing, then there are m * n ways to do both things together.
In this problem, the eighteen-sided die is rolled three times. Since there are 18 possible outcomes for each roll, there are 18 ways to roll the die the first time, 18 ways to roll the die the second time, and 18 ways to roll the die the third time. By applying the multiplication principle, we can calculate the total number of ways to roll the die three times as:
18 * 18 * 18 = 5832
Therefore, there are 5832 ways in which the die can be rolled three times.
To solve this problem, we need to find the number of ways the eighteen-sided die can be rolled three times.
To calculate the total number of outcomes, we use the principle of multiplication. Since each roll is independent, we multiply the number of outcomes for each roll.
Since there are 18 sides on the die, there are 18 possible outcomes for each roll. So we have:
Number of outcomes for the first roll = 18
Number of outcomes for the second roll = 18
Number of outcomes for the third roll = 18
To find the total number of outcomes, we multiply these numbers together:
Total number of outcomes = 18 * 18 * 18
Simplifying this expression, we get:
Total number of outcomes = 18^3
Therefore, there are 18^3 = 5,832 ways the eighteen-sided die can be rolled three times.