Understanding the Problem
To determine how many numbers can be formed between 100 and 1000 using the digits 1, 2, 3, 4, 5, 6, and 7, we need to create three-digit numbers. The hundreds, tens, and units places must be filled using the available digits.
Conditions to Consider
- All digits must be chosen from 1 to 7.
- The first digit (hundreds place) cannot be zero.
- Each digit can be used only once in a number.
Calculating the Possibilities
1. Choosing the Hundreds Place:
- The first digit can be any of the 7 digits (1 to 7).
- Total choices for the hundreds place = 7.
2. Choosing the Tens Place:
- After selecting the hundreds digit, we can choose from the remaining 6 digits.
- Total choices for the tens place = 6.
3. Choosing the Units Place:
- After selecting both the hundreds and tens digits, we have 5 digits left to choose from.
- Total choices for the units place = 5.
Calculating Total Combinations
- The total number of combinations can be calculated by multiplying the choices for each place:
- Total combinations = Choices for hundreds × Choices for tens × Choices for units
- Total combinations = 7 × 6 × 5 = 210.
Conclusion
The total number of three-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, 6, and 7 while lying between 100 and 1000 is 210.