Permutation with Repetition Calculator
Discover the number of unique arrangements when you have repeated items.
Input Values
Enter the total number of objects and the counts of each repeated object to calculate permutations with repetition.
Enter comma-separated values for each repetition count.
Result:
Formula & Visualization
Where:
- n is the total number of objects.
- n1, n2, ..., nk are the counts of each type of identical object.
- P is the total number of distinct permutations.
Calculation Breakdown:
What are Permutations with Repetition?
Permutations with repetition are arrangements of objects where some objects are identical. Unlike simple permutations where all objects are distinct, here we account for repetitions to find the number of unique arrangements. For example, if you want to arrange the letters in the word "banana", you have repeated 'a's and 'n's. This calculator helps you find out how many distinct ways you can arrange such objects.
To use this calculator, enter the total number of items you have, and then specify the count of each type of repeated item separated by commas. For instance, for "banana", you have 6 total letters, with 'a' repeating 3 times and 'n' repeating 2 times. Input '6' as total objects and '3,2' as repetitions. The calculator will then give you the number of unique permutations.
Learn more about permutations and combinations on websites like Math is Fun or Khan Academy.