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Probability is the study of how likely an event is to happen. It tells us about the chances of different outcomes. In combinatorics, like in the case of license plates, we calculate the total possible outcomes to find the probability of a specific configuration.Consider each license plate as an event. You want to know how many different plates are possible. This is an example of working out probability without needing to focus on specific conditions or constraints that change the likelihood of outcomes. Here, each number (0-9) and letter (A-Z) is equally likely, showing a uniform distribution.The principles of probability involve counting the total outcomes possible, and then considering how many ways an event can occur. For instance:

• For numbers, since each digit has 10 outcomes, you multiply these: \(10 \times 10 \times 10\)
• For letters, each letter has 26 outcomes: \(26 \times 26 \times 26\)

By multiplying these, you ensure that each possible number-letter pairing is covered, resulting in 17,576,000 possible combinations.

Mathematical calculation involves using numerical and algebraic processes to reach a solution. It's essential for solving problems related to almost every field, including the creation of license plates.In calculating the total number of different license plates, we use basic multiplication due to the choices available for each digit and letter.### Number CalculationFirst, for the numbers, each of the 3 slots can be any digit from 0 to 9, giving 10 choices per slot. The calculation is straightforward:\[10 \times 10 \times 10 = 10^3 = 1000\]### Letter CalculationSimilarly, for the letters, each of the 3 slots can be any letter from A to Z, giving 26 choices per slot. We calculate: \[26 \times 26 \times 26 = 26^3 = 17,576\]Finally, combining these two large results to get the total number of possible plates:\[1000 \times 17,576 = 17,576,000\]These steps exhibit how we apply mathematical calculations to solve problems in combinatorics efficiently.

Problem solving in mathematics often requires breaking a problem into manageable steps, just like solving for the number of license plates. ### Step-by-Step Approach 1. **Understand the Problem:** Know what the question asks. Here, it's about finding total license plates. 2. **Break It Down:** Separate the problem into smaller parts. Calculate possible outcomes for numbers and letters separately. 3. **Solve Each Part:** Use basic principles to find total outcomes for each segment. 4. **Combine Solutions:** Connect your individual answers into a final solution. Problem solving is more effective when you understand the logic behind each step. Unlike guesswork, it provides clear, logical outcomes based on specific calculations and principles, as demonstrated in solving for potential license plate combinations.