Question
Georgia license plates consist of 3 letters and 4 numbers. Each letter and number can repeat. How many different license plates can be made?
Question 5 options:
115,316,136
175,760,000
102,351,600
156,000,000
Question 5 options:
115,316,136
175,760,000
102,351,600
156,000,000
Answers
GPT-4o mini
To find the total number of different license plates that can be created in Georgia, we need to calculate the combinations of letters and numbers based on the given requirements.
1. **Letters**: There are 3 letters in the license plate, and each letter can be any of the 26 letters in the English alphabet. Since repetition is allowed, the total number of combinations for the letters is:
\[
26 \times 26 \times 26 = 26^3 = 17,576
\]
2. **Numbers**: There are 4 numbers in the license plate, and each number can be any digit from 0 to 9. Again, since repetition is allowed, the total number of combinations for the numbers is:
\[
10 \times 10 \times 10 \times 10 = 10^4 = 10,000
\]
3. **Total Combinations**: The total number of different license plates is the product of the combinations of letters and numbers:
\[
26^3 \times 10^4 = 17,576 \times 10,000 = 175,760,000
\]
Therefore, the total number of different license plates that can be made in Georgia is **175,760,000**.
The correct answer is:
**175,760,000**
1. **Letters**: There are 3 letters in the license plate, and each letter can be any of the 26 letters in the English alphabet. Since repetition is allowed, the total number of combinations for the letters is:
\[
26 \times 26 \times 26 = 26^3 = 17,576
\]
2. **Numbers**: There are 4 numbers in the license plate, and each number can be any digit from 0 to 9. Again, since repetition is allowed, the total number of combinations for the numbers is:
\[
10 \times 10 \times 10 \times 10 = 10^4 = 10,000
\]
3. **Total Combinations**: The total number of different license plates is the product of the combinations of letters and numbers:
\[
26^3 \times 10^4 = 17,576 \times 10,000 = 175,760,000
\]
Therefore, the total number of different license plates that can be made in Georgia is **175,760,000**.
The correct answer is:
**175,760,000**