Question
How many phone numbers are possible in the (770) area code if: For the form ABC-XXXX, A is restricted to numbers 2-8, but B, C, and X can be any digit 0-9, including repetitions.
Question 2 options:
3,188,646
7,000,000
6,000,000
3,720,087
Question 2 options:
3,188,646
7,000,000
6,000,000
3,720,087
Answers
GPT-4o mini
To calculate the total number of possible phone numbers in the (770) area code in the format ABC-XXXX, we need to consider the restrictions for each digit:
1. **A**: This digit can be any number from 2 to 8 (inclusive). Therefore, the possible values for A are: 2, 3, 4, 5, 6, 7, 8. This gives us a total of **7 options** for A.
2. **B**: This digit can be any digit from 0 to 9. Therefore, there are **10 options** for B.
3. **C**: This digit can also be any digit from 0 to 9. There are again **10 options** for C.
4. **XXXX**: Each of the four digits (X) can be any digit from 0 to 9. Each X also has **10 options**. So for XXXX, there are:
- \(10 \times 10 \times 10 \times 10 = 10^4 = 10,000\) options.
Now we multiply the options together:
\[
\text{Total phone numbers} = \text{options for A} \times \text{options for B} \times \text{options for C} \times \text{options for XXXX}
\]
Substituting in the numbers:
\[
\text{Total phone numbers} = 7 \times 10 \times 10 \times 10,000
\]
\[
= 7 \times 10 \times 10^3
\]
\[
= 7 \times 10^4
\]
\[
= 7 \times 10,000 = 70,000
\]
Calculating step by step again:
1. For A: 7 options (2-8)
2. For B: 10 options (0-9)
3. For C: 10 options (0-9)
4. For XXXX: 10,000 options
Now let's put it all together:
\[
7 \times 10 \times 10 \times 10,000 = 7 \times 100,000 = 700,000
\]
So there are **700,000** possible phone numbers in the (770) area code with the given restrictions.
Thus, none of the options provided (3,188,646; 7,000,000; 6,000,000; 3,720,087) are correct for this formula. The expected result is **700,000**.
If you can clarify the question further or if there are additional constraints, please provide more details.
1. **A**: This digit can be any number from 2 to 8 (inclusive). Therefore, the possible values for A are: 2, 3, 4, 5, 6, 7, 8. This gives us a total of **7 options** for A.
2. **B**: This digit can be any digit from 0 to 9. Therefore, there are **10 options** for B.
3. **C**: This digit can also be any digit from 0 to 9. There are again **10 options** for C.
4. **XXXX**: Each of the four digits (X) can be any digit from 0 to 9. Each X also has **10 options**. So for XXXX, there are:
- \(10 \times 10 \times 10 \times 10 = 10^4 = 10,000\) options.
Now we multiply the options together:
\[
\text{Total phone numbers} = \text{options for A} \times \text{options for B} \times \text{options for C} \times \text{options for XXXX}
\]
Substituting in the numbers:
\[
\text{Total phone numbers} = 7 \times 10 \times 10 \times 10,000
\]
\[
= 7 \times 10 \times 10^3
\]
\[
= 7 \times 10^4
\]
\[
= 7 \times 10,000 = 70,000
\]
Calculating step by step again:
1. For A: 7 options (2-8)
2. For B: 10 options (0-9)
3. For C: 10 options (0-9)
4. For XXXX: 10,000 options
Now let's put it all together:
\[
7 \times 10 \times 10 \times 10,000 = 7 \times 100,000 = 700,000
\]
So there are **700,000** possible phone numbers in the (770) area code with the given restrictions.
Thus, none of the options provided (3,188,646; 7,000,000; 6,000,000; 3,720,087) are correct for this formula. The expected result is **700,000**.
If you can clarify the question further or if there are additional constraints, please provide more details.