Four-digit numbers are a special class of numbers that are composed of four digits. They are commonly used in many areas, such as identification numbers, security codes, PIN numbers, and even in some lottery games. In this article, we will discuss how many four-digit numbers can be formed with the digits 1, 2, and 3.

## Overview of 4-Digit Numbers

Four-digit numbers are composed of four distinct digits, each of which can range from 0 to 9. The numbers can be arranged in any order, so the same number can be expressed in different ways. For example, the number 1234 can also be written as 2341 or 3412.

The range of possible four-digit numbers is 0000 to 9999. As such, there are a total of 10,000 possible four-digit numbers.

## Counting Combinations of 1, 2, 3

When we are only given the digits 1, 2, and 3, we can use basic math and logic to determine how many combinations of four-digit numbers can be formed.

First, we must consider how many unique combinations of four-digit numbers can be formed with the given digits. To do this, we can use the formula for permutations, which is nPr = n! / (n-r)!. In this case, n = 3 (the number of given digits) and r = 4 (the number of digits in the number). This gives us a result of 3! / (3-4)! = 3! / -1! = 3! = 6.

This means that there are six unique combinations of four-digit numbers that can be formed with the digits 1, 2, and 3. The six combinations are: 1234, 1243, 1324, 1342, 1423, and 1432.

In conclusion, there are six unique combinations of four-digit numbers that can be formed with the digits 1, 2, and 3. This is a relatively small number compared to the 10,000 possible four-digit numbers, but it can still be useful in certain scenarios, such as creating identification numbers or security codes.

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