What are the possible combinations of 1, 2, 3, 4 and 5?

The numbers 1, 2, 3, 4, and 5 seem deceptively simple, but they hide a surprisingly rich world of mathematical arrangements beneath the surface.

This guide walks you through every possible way to combine and arrange these five digits, from quick two-number pairs to full five-digit sequences with clear examples, real-world context, and exact counts.

Table of Contents

• Unique Combinations of 1, 2, 3, 4 and 5
• Full Permutations of All 5 Digits
• All 120 Permutations Listed

Unique Combinations of 1, 2, 3, 4 and 5

A combination is about what you pick, not the sequence you pick it in. We're looking at every possible non-empty subset of the numbers {1, 2, 3, 4, 5}.

The total number of non-empty subsets from a set of 5 elements is 2⁵ − 1 = 31.

Here's every single combination organized by group size:

1 - Number Groups: 5 Combinations

These are the simplest selections: just one number at a time i.e., singletons 

{1}, {2}, {3}, {4}, {5}

2 - Number Groups: 10 Combinations

Every possible pair from the five numbers:

{1,2}, {1,3}, {1,4}, {1,5}, {2,3}, {2,4}, {2,5}, {3,4}, {3,5}, {4,5}

Note: {1,2} and {2,1} are listed only once, because in combinations, they're the same pair.

3 - Number Groups: 10 Combinations

Every possible trio:

{1,2,3}, {1,2,4}, {1,2,5}, {1,3,4}, {1,3,5}, {1,4,5}, {2,3,4}, {2,3,5}, {2,4,5}, {3,4,5}

4 - Number Groups: 5 Combinations

Every group of four :

{1,2,3,4}, {1,2,3,5}, {1,2,4,5}, {1,3,4,5}, {2,3,4,5}

5 - Number Group: 1 Combination

There's only one way to select all five numbers at once:

{1, 2, 3, 4, 5}

Full Permutations of All 5 Digits 

To arrange all 5 numbers in a sequence, you use the factorial formula:

5! = 5 × 4 × 3 × 2 × 1 = 120

There are exactly 120 unique arrangements of the digits 1, 2, 3, 4, and 5 when each digit is used exactly once.

Here's a quick intuition for why:

• You have 5 choices for the first position

• Then 4 remaining choices for the second

• Then 3 for the third, 2 for the fourth, and only 1 left for the fifth

• Multiply them together: 5 × 4 × 3 × 2 × 1 = 120

All 120 Permutations Listed 

Below are all 120 full arrangements of 1, 2, 3, 4, 5 (grouped in rows of 10 for readability):

12345  12354  12435  12453  12534  12543  13245  13254  13425  13452

13524  13542  14235  14253  14325  14352  14523  14532  15234  15243

15324  15342  15423  15432  21345  21354  21435  21453  21534  21543

23145  23154  23415  23451  23514  23541  24135  24153  24315  24351

24513  24531  25134  25143  25314  25341  25413  25431  31245  31254

31425  31452  31524  31542  32145  32154  32415  32451  32514  32541

34125  34152  34215  34251  34512  34521  35124  35142  35214  35241

35412  35421  41235  41253  41325  41352  41523  41532  42135  42153

42315  42351  42513  42531  43125  43152  43215  43251  43512  43521

45123  45132  45213  45231  45312  45321  51234  51243  51324  51342

51423  51432  52134  52143  52314  52341  52413  52431  53124  53142

53214  53241  53412  53421  54123  54132  54213  54231  54312  54321

 

The five numbers 1, 2, 3, 4, and 5 can produce 31 unique combinations (when order doesn't matter) or 120 full permutations (when order does matter). Shorter arrangements using fewer than all five digits add up to 325 ordered sequences in total. Whether you're studying for a math exam, building a probability model, or just solving a puzzle, these numbers and the patterns they create are a perfect starting point for understanding combinatorics in a concrete, hands-on way.