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:
3,720,087
3,188,646
6,000,000
7,000,000
Question 2 options:
3,720,087
3,188,646
6,000,000
7,000,000
Answers
GPT-4o mini
To find how many phone numbers are possible in the (770) area code given the restrictions for the format ABC-XXXX, we can break down the options you provided:
1. **A** (the first digit of ABC) can be any digit from 2 to 8. This gives us 7 options for A:
- Possible values: 2, 3, 4, 5, 6, 7, 8.
Therefore, there are 7 choices for A.
2. **B** (the second digit of ABC) can be any digit from 0 to 9. This gives us 10 options for B:
- Possible values: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Therefore, there are 10 choices for B.
3. **C** (the third digit of ABC) can also be any digit from 0 to 9. So, there are again 10 options for C.
Therefore, there are 10 choices for C.
4. **XXXX** (the last four digits of the phone number) can also each be any digit from 0 to 9. For each of those four X's, there are 10 options. Since there are four positions, the total number of combinations for XXXX is \(10^4\).
Therefore, there are \(10 \times 10 \times 10 \times 10 = 10^4 = 10,000\) choices for XXXX.
Now we multiply the number of choices for each digit together:
- Choices for A: 7
- Choices for B: 10
- Choices for C: 10
- Choices for XXXX: 10,000
So, the total number of possible phone numbers is:
\[
7 \times 10 \times 10 \times 10,000 = 7 \times 10^3 \times 10^4 = 7 \times 10^7 = 7,000,000
\]
Thus, the answer is **7,000,000**.
1. **A** (the first digit of ABC) can be any digit from 2 to 8. This gives us 7 options for A:
- Possible values: 2, 3, 4, 5, 6, 7, 8.
Therefore, there are 7 choices for A.
2. **B** (the second digit of ABC) can be any digit from 0 to 9. This gives us 10 options for B:
- Possible values: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Therefore, there are 10 choices for B.
3. **C** (the third digit of ABC) can also be any digit from 0 to 9. So, there are again 10 options for C.
Therefore, there are 10 choices for C.
4. **XXXX** (the last four digits of the phone number) can also each be any digit from 0 to 9. For each of those four X's, there are 10 options. Since there are four positions, the total number of combinations for XXXX is \(10^4\).
Therefore, there are \(10 \times 10 \times 10 \times 10 = 10^4 = 10,000\) choices for XXXX.
Now we multiply the number of choices for each digit together:
- Choices for A: 7
- Choices for B: 10
- Choices for C: 10
- Choices for XXXX: 10,000
So, the total number of possible phone numbers is:
\[
7 \times 10 \times 10 \times 10,000 = 7 \times 10^3 \times 10^4 = 7 \times 10^7 = 7,000,000
\]
Thus, the answer is **7,000,000**.