組み合わせと順列
すべての可能な組み合わせと順列を生成アイテムリストから。順序が重要でない場合は組み合わせを、順序が重要な場合は順列を選択してください。
各組み合わせのアイテム数
アイテムを入力して「組み合わせを生成」をクリックして結果を表示
Combinations
Combinations are selections where order doesn't matter. Selecting items A, B is the same as selecting B, A.
Formula: C(n,r) = n! / (r! × (n-r)!)
Where n = total items, r = items to choose
Example: Choose 2 from [A, B, C]
All Possible Combinations: AB, AC, BC (3 combinations)
Note: AB = BA (same combination)
Permutations
Permutations are arrangements where order matters. Selecting items A, B is different from selecting B, A.
Formula: P(n,r) = n! / (n-r)!
Where n = total items, r = items to arrange
Example: Arrange 2 from [A, B, C]
All Possible Permutations: AB, AC, BA, BC, CA, CB (6 permutations)
Note: AB ≠ BA (different arrangements)
Combination Use Cases:
- • Selecting team members from a group
- • Choosing pizza toppings
- • Product feature combinations
- • Lottery number selection
- • Committee formation
Permutation Use Cases:
- • Arranging people in a line
- • Password generation
- • Race finishing positions
- • Seating arrangements
- • Tournament brackets
Quick Examples:
• 5 people, choose 2: 5C2 = 10 combinations
• 4 colors, choose 3: 4C3 = 4 combinations
• 5 people, arrange 2: 5P2 = 20 permutations
• 4 colors, arrange 3: 4P3 = 24 permutations
When should I choose combinations vs permutations?
Choose combinations when the order of selection doesn't matter (like choosing team members). Choose permutations when the order is important (like arranging people in a specific sequence).
Why is there a 1000 result limit?
Large sets can generate millions of combinations or permutations. The 1000 limit ensures fast performance while still showing you the total count and first 1000 results for analysis.
How do the mathematical formulas work?
Combinations: C(n,r) = n! / (r! × (n-r)!) - divides out arrangements to count only selections.
Permutations: P(n,r) = n! / (n-r)! - counts all possible arrangements of selected items.
Can I use this for large datasets?
Yes, but be aware that combinations and permutations grow exponentially. For example, choosing 10 items from 20 gives 184,756 combinations. The tool will show you the exact count before generating.
What input formats are supported?
You can enter items separated by new lines, commas, or semicolons. The tool automatically detects and parses your input format, removing empty entries and trimming whitespace.