Math Problem Statement

Using the digits 1,2,3,4,5 to create a 4 digit number sequence by combining two of the digits at the end of the sequence, the last two digits, example; 1, 2, 3, 45 or 2, 3,4, 51 or 4, 5, 1, 23...list all possible combinations in order

Solution

To generate all possible combinations of four-digit numbers using the digits 1, 2, 3, 4, and 5, where the last two digits are combined to form a two-digit number, we can follow a systematic approach:

  • The first two digits are selected from the digits 1 to 5.
  • The last two digits are combined to form a two-digit number, either by using two digits from the set of digits (1 to 5).

Here are all the possible combinations in order:

Case 1: Last two digits form the number 12

  1. 3, 4, 12
  2. 3, 5, 12
  3. 4, 3, 12
  4. 5, 4,

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Permutations
Number Theory

Formulas

n! (Factorial) for calculating permutations

Theorems

Basic Counting Principle

Suitable Grade Level

Grades 6-8

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