Statistics & Probability

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Permutation with Repetition Calculator.

Calculate ordered selections with replacement using nʳ.

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Set your values

Results update as you type.

02 / ANSWER

Choices (n)

Positions (r)

permutations

1,000.000000

Results update automatically as you type.

Use Cases

Counting password combinations

Determine how many different passwords of a certain length can be created using a set of characters, where characters can repeat.

Example: With 10 possible digits and a 4-digit PIN, there are 10^4 = 10,000 combinations.

Analyzing multiple-choice tests

Calculate the number of possible answer sequences for a test with multiple questions, each having the same number of answer choices.

Example: A 5-question quiz with 4 options each yields 4^5 = 1,024 possible answer sheets.

Frequently Asked Questions

What is a permutation with repetition?: A permutation with repetition counts the number of ways to arrange r items chosen from n types, where each type can be used more than once. The formula is n^r.
How do I use this calculator?: Enter the number of choices (n) and the number of positions (r). The calculator will compute n raised to the power of r, giving the total number of ordered selections with replacement.
What does 'with replacement' mean?: With replacement means that after selecting an item, you put it back, so the same item can be chosen again for the next position. This allows repetitions in the sequence.

Tips & Common Mistakes

Tips

Ensure n and r are non-negative integers. The calculator expects whole numbers for both fields.
If r is 0, the result is 1, because there is exactly one way to arrange zero items.
For large values of n and r, the result can be extremely large; the calculator may display it in scientific notation.
Remember that this calculator is for ordered selections with repetition, not for combinations or permutations without repetition.

Common Mistakes to Avoid

Confusing this with permutations without repetition, where the formula is n!/(n-r)! and repetition is not allowed.
Entering negative numbers or decimals, which are not valid for counting choices and positions.
Assuming the result is the number of unique sets (combinations) rather than ordered sequences.

Last updated: August 13, 2026

Use Cases

Counting password combinations

Determine how many different passwords of a certain length can be created using a set of characters, where characters can repeat.

Example: With 10 possible digits and a 4-digit PIN, there are 10^4 = 10,000 combinations.

Analyzing multiple-choice tests

Calculate the number of possible answer sequences for a test with multiple questions, each having the same number of answer choices.

Example: A 5-question quiz with 4 options each yields 4^5 = 1,024 possible answer sheets.

Frequently Asked Questions

What is a permutation with repetition?

A permutation with repetition counts the number of ways to arrange r items chosen from n types, where each type can be used more than once. The formula is n^r.

How do I use this calculator?

Enter the number of choices (n) and the number of positions (r). The calculator will compute n raised to the power of r, giving the total number of ordered selections with replacement.

What does 'with replacement' mean?

With replacement means that after selecting an item, you put it back, so the same item can be chosen again for the next position. This allows repetitions in the sequence.

Tips & Common Mistakes

Tips

Ensure n and r are non-negative integers. The calculator expects whole numbers for both fields.
If r is 0, the result is 1, because there is exactly one way to arrange zero items.
For large values of n and r, the result can be extremely large; the calculator may display it in scientific notation.
Remember that this calculator is for ordered selections with repetition, not for combinations or permutations without repetition.

Common Mistakes to Avoid

Confusing this with permutations without repetition, where the formula is n!/(n-r)! and repetition is not allowed.
Entering negative numbers or decimals, which are not valid for counting choices and positions.
Assuming the result is the number of unique sets (combinations) rather than ordered sequences.

Use Cases

Counting password combinations

Determine how many different passwords of a certain length can be created using a set of characters, where characters can repeat.

Example: With 10 possible digits and a 4-digit PIN, there are 10^4 = 10,000 combinations.

Analyzing multiple-choice tests

Calculate the number of possible answer sequences for a test with multiple questions, each having the same number of answer choices.

Example: A 5-question quiz with 4 options each yields 4^5 = 1,024 possible answer sheets.

Frequently Asked Questions

What is a permutation with repetition?

A permutation with repetition counts the number of ways to arrange r items chosen from n types, where each type can be used more than once. The formula is n^r.

How do I use this calculator?

Enter the number of choices (n) and the number of positions (r). The calculator will compute n raised to the power of r, giving the total number of ordered selections with replacement.

What does 'with replacement' mean?

With replacement means that after selecting an item, you put it back, so the same item can be chosen again for the next position. This allows repetitions in the sequence.

Tips & Common Mistakes

Tips

Ensure n and r are non-negative integers. The calculator expects whole numbers for both fields.
If r is 0, the result is 1, because there is exactly one way to arrange zero items.
For large values of n and r, the result can be extremely large; the calculator may display it in scientific notation.
Remember that this calculator is for ordered selections with repetition, not for combinations or permutations without repetition.

Common Mistakes to Avoid

Confusing this with permutations without repetition, where the formula is n!/(n-r)! and repetition is not allowed.
Entering negative numbers or decimals, which are not valid for counting choices and positions.
Assuming the result is the number of unique sets (combinations) rather than ordered sequences.