a liscense plate that has 3 numbers from 0-9 and 2 letters where each number and a letter may be used more than once. Find the Fundamental Counting Principle to find the number of outcomes in the situation
To find the number of outcomes in this situation, we can use the Fundamental Counting Principle. The Fundamental Counting Principle states that if there are n_1 ways to do the first task, and for each of those ways there are n_2 ways to do the second task, and so on, then there are n_1 * n_2 * ... * n_k ways to do all k tasks.
In this specific case, we have 3 numbers (0-9) and 2 letters. Since each number and letter can be used more than once, we have 10 choices for each of the three numbers and 26 choices for each of the two letters.
Therefore, using the Fundamental Counting Principle, we multiply the number of choices for each part:
Number of outcomes = (number of choices for the first number) * (number of choices for the second number) * (number of choices for the third number) * (number of choices for the first letter) * (number of choices for the second letter)
Number of outcomes = 10 * 10 * 10 * 26 * 26
Calculating this, we find that there are 1,690,000 possible outcomes for the license plate with 3 numbers (0-9) and 2 letters where each number and letter may be used more than once.