Understanding the Problem
To find the numbers between 10 and 1000 that can be formed using the digits 1, 2, 3, 4, 5, 6, and 7, we can categorize them based on the number of digits: two-digit and three-digit numbers.
Two-Digit Numbers
- The range of two-digit numbers is from 10 to 99.
- The first digit can be any of the digits 1 through 7 (7 options).
- The second digit can also be any of the digits 1 through 7 (7 options).
- Total two-digit numbers = 7 (choices for the first digit) × 7 (choices for the second digit) = 49.
Three-Digit Numbers
- The range of three-digit numbers is from 100 to 999.
- The first digit can again be any of the digits 1 through 7 (7 options).
- The second digit can also be any of the digits 1 through 7 (7 options).
- The third digit can also be any of the digits 1 through 7 (7 options).
- Total three-digit numbers = 7 (choices for the first digit) × 7 (choices for the second digit) × 7 (choices for the third digit) = 343.
Final Calculation
- Total numbers between 10 and 1000 = Total two-digit numbers + Total three-digit numbers
- Total = 49 (two-digit) + 343 (three-digit) = 392.
Conclusion
The total number of numbers that can be formed with the digits 1, 2, 3, 4, 5, 6, and 7, lying between 10 and 1000, is 392.