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 7 options:
175,760,000
102,351,600
115,316,136
156,000,000
Question 7 options:
175,760,000
102,351,600
115,316,136
156,000,000
Answers
GPT-4o mini
To determine the total number of different license plates that can be created with Georgia's format of 3 letters followed by 4 numbers, we can break it down into two parts: the letters and the numbers.
1. **Calculating the number of combinations for the letters:**
- There are 26 letters in the English alphabet.
- Since each letter can repeat and we need 3 letters, the total combinations for the letters is:
\[
26 \times 26 \times 26 = 26^3 = 17,576
\]
2. **Calculating the number of combinations for the numbers:**
- There are 10 digits (0 through 9).
- Since each number can repeat and we need 4 numbers, the total combinations for the numbers is:
\[
10 \times 10 \times 10 \times 10 = 10^4 = 10,000
\]
3. **Combining both parts to find the total combinations of license plates:**
- The total number of different license plates is the product of the combinations of letters and numbers:
\[
\text{Total combinations} = \text{Combinations of letters} \times \text{Combinations of numbers} = 17,576 \times 10,000
\]
- Calculating this gives:
\[
17,576 \times 10,000 = 175,760,000
\]
Thus, the total number of different license plates that can be made is **175,760,000**.
The correct answer is:
**175,760,000**
1. **Calculating the number of combinations for the letters:**
- There are 26 letters in the English alphabet.
- Since each letter can repeat and we need 3 letters, the total combinations for the letters is:
\[
26 \times 26 \times 26 = 26^3 = 17,576
\]
2. **Calculating the number of combinations for the numbers:**
- There are 10 digits (0 through 9).
- Since each number can repeat and we need 4 numbers, the total combinations for the numbers is:
\[
10 \times 10 \times 10 \times 10 = 10^4 = 10,000
\]
3. **Combining both parts to find the total combinations of license plates:**
- The total number of different license plates is the product of the combinations of letters and numbers:
\[
\text{Total combinations} = \text{Combinations of letters} \times \text{Combinations of numbers} = 17,576 \times 10,000
\]
- Calculating this gives:
\[
17,576 \times 10,000 = 175,760,000
\]
Thus, the total number of different license plates that can be made is **175,760,000**.
The correct answer is:
**175,760,000**