4. Probability
Fundamental Counting Principle
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How many options are there for license plates with any three letters (A-Z) followed by any 3 numbers (0-9)?
A
B
C
D
Verified step by step guidance1
First, determine the number of possible combinations for the letters. Since there are 26 letters in the alphabet (A-Z), and the license plate requires three letters, calculate the number of combinations by raising 26 to the power of 3.
Use the formula for combinations: \( 26^3 \). This represents the total number of ways to arrange three letters.
Next, determine the number of possible combinations for the numbers. Since there are 10 digits (0-9), and the license plate requires three numbers, calculate the number of combinations by raising 10 to the power of 3.
Use the formula for combinations: \( 10^3 \). This represents the total number of ways to arrange three numbers.
Finally, multiply the number of combinations for the letters by the number of combinations for the numbers to find the total number of possible license plates: \( 26^3 \times 10^3 \).
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