Problem
Using the numbers 1, 2, 3, and 4, which different three-digit numbers can be formed without repeating any digits? Try to write them down and think about how to ensure that you neither repeat nor miss any numbers during the process.
Analysis
To form a three-digit number, you need to use three of the numbers. Any digit in this three-digit number can be any one of the numbers 1, 2, 3, or 4. Therefore, there are many three-digit numbers that can be formed using these four numbers. In order to ensure no repetition and no omissions, we can write them down in a certain order sequentially.
Solutions
(1) If the digit in the hundreds place is 1, the following three-digit numbers can be formed: 123, 124, 132, 134, 142, 143.Â
(2) If the digit in the hundreds place is 2, the following three-digit numbers can be formed: 213, 214, 231, 234, 241, 243.Â
(3) If the digit in the hundreds place is 3, the following three-digit numbers can be formed: 312, 314, 321, 324, 341, 342.Â
(4) If the digit in the hundreds place is 4, the following three-digit numbers can be formed: 412, 413, 421, 423, 431, 432.