Permutation & Combination Calculator

Name: Permutation & Combination Calculator
Author: Jitendra Kumar

Calculate nPr, nCr, factorials, circular arrangements, and repetition-based counting formulas with exact counts and compact large-number output.

Last Updated: May 2026

Counting method

Total items (n)

Number of distinct available items or categories.

Items selected (r)

Number of items chosen or ordered.

Combinations

2,598,960

Approximation

2.598960e+6

Digits

Formula

nCr = n! / (r!(n-r)!)

Step	Value
Formula	nCr = n! / (r!(n-r)!)
Substitution	52C5 = 52! / (5!(52-5)!)
Order matters?	No
Repetition allowed?	No
Interpretation	Choose 5 items from 52 when order does not matter.

Exact result

2,598,960

Order matters

Use permutations when ABC and BAC are different outcomes, such as rankings or codes.

Order ignored

Use combinations when ABC and BAC are the same group, such as teams or card hands.

Repetition

Select a repetition mode when an item can be used more than once, such as PIN digits.

Counting setup check

Decide order and repetition before calculating. Most mistakes in counting problems come from choosing nPr when nCr is needed, or treating repeated choices as if they were not allowed.

Counting Method Notice

This calculator is for educational and planning use. Counting results depend on the correct assumptions about distinct items, order, repetition, circular equivalence, and replacement rules.

Reviewed For Methodology, Labels, And Sources

Every CalculatorWallah calculator is published with visible update labeling, linked source references, and founder-led review of formula clarity on trust-sensitive topics. Use results as planning support, then verify institution-, policy-, or jurisdiction-specific rules where they apply.

Reviewed By

Jitendra Kumar, Founder & Editorial Standards Lead, oversees methodology standards and trust-sensitive publishing decisions.

Review editor profile

Topic Ownership

Sales tax and tax-sensitive estimate tools, Education and GPA planning calculators, Health, protein, and screening-formula pages, Platform-wide publishing standards and methodology

See ownership standards

Methodology & Updates

Page updated May 2026. Trust-critical pages are reviewed when official rates or rules change. Evergreen calculator guides are checked on a recurring quarterly or annual cycle depending on topic volatility.

Sources & methodology About the review process

How to Use the Permutation & Combination Calculator

Choose the counting method first. Use combinations when order does not matter, permutations when order matters, and repetition modes when an item can be reused.

Enter total items as n and selected items as r. Factorial and circular permutation modes use only n.

Step 1: Choose the counting method
Select nCr, nPr, repetition, factorial, or circular permutation mode.
Step 2: Enter n and r
Use n for total available items and r for how many are selected or arranged.
Step 3: Review the count
Check the exact result, approximation, digit count, and formula substitution.
Step 4: Confirm assumptions
Use the order/repetition notes to verify the selected counting model.

How This Permutation & Combination Calculator Works

The calculator applies the counting formula that matches the selected method. For standard combinations and permutations, it assumes distinct items and no repetition.

Repetition modes change the formula because selected items can be reused. Circular permutation mode treats rotations around a circle as the same arrangement, so it uses one fewer factorial.

Results are calculated as exact integers when practical. Very large outputs are shown with digit counts and scientific notation so the result stays readable.

Permutation and Combination Guide

Core Counting Formulas

Method	Formula	Use
Combination	nCr = n! / (r!(n-r)!)	Order does not matter, no repetition.
Permutation	nPr = n! / (n-r)!	Order matters, no repetition.
Combination with repetition	C(n+r-1, r)	Order does not matter, repetition allowed.
Permutation with repetition	n^r	Order matters, repetition allowed.
Factorial	n!	Arrange all n distinct items in a line.
Circular permutation	(n - 1)!	Arrange n distinct items around a circle when rotations match.

Choosing the Right Method

Scenario	Order matters?	Repetition?	Use
Choosing a committee	No	No	Combination
Ranking top finishers	Yes	No	Permutation
Creating a PIN code	Yes	Yes	Permutation with repetition
Choosing scoops from flavors	No	Yes	Combination with repetition
Arranging people around a table	Yes, circular	No	Circular permutation

The key question is whether a different order creates a different outcome. If a team of Alex, Blair, and Casey is the same team in any order, use a combination. If first, second, and third place are different outcomes, use a permutation.

Once you have a count, it can become the denominator of a probability problem. Use the probability calculator to turn favorable counts into event probabilities, complements, or binomial results.

Keep the research moving with Probability Calculator, Statistics Calculator, Fraction Calculator, and Scientific Calculator.