Permutation and Combination Calculator
What is Permutation?
A permutation is an arrangement of objects where the order matters.
The formula for permutation is:
nPr = n! / (n − r)!
For example, if n = 5 and r = 2:
5P2 = 5! / (5 − 2)!
5P2 = 5! / 3! = 20
Therefore, there are 20 possible arrangements.
What is Combination?
A combination is a selection of objects where the order does not matter.
The formula for combination is:
nCr = n! / [r! × (n − r)!]
For example, if n = 5 and r = 2:
5C2 = 5! / (2! × 3!)
5C2 = 10
Therefore, there are 10 possible combinations.
Difference Between Permutation and Combination
The main difference is whether the order of selection matters.
| Feature | Permutation | Combination |
|---|---|---|
| Order matters | Yes | No |
| Formula | n!/(n-r)! | n!/[r!(n-r)!] |
| Example | Arranging people | Selecting people |
| Notation | nPr | nCr |
For example, selecting A and B is the same combination as B and A. However, in permutations, AB and BA are different arrangements.
How to Use the Calculator
Using the Permutation and Combination Calculator is simple:
- Enter the value of n.
- Enter the value of r.
- Click the Calculate button.
- The calculator displays both nPr and nCr.
- Use the Reset button to perform another calculation.
The calculator also validates the input and ensures that r is not greater than n.
Why Use a Permutation and Combination Calculator?
Calculating factorials manually can become difficult when dealing with large numbers. This calculator makes the process faster and reduces calculation errors.
It can be useful for:
- Mathematics homework
- Probability problems
- Statistics
- Combinatorics
- Competitive examinations
- Computer science
- Data analysis
- Arrangement and selection problems
Frequently Asked Questions
What is nPr?
nPr represents the number of ways to arrange r objects selected from n objects, where the order matters.
What is nCr?
nCr represents the number of ways to select r objects from n objects, where the order does not matter.
Can r be greater than n?
No. In standard permutation and combination calculations, r must be less than or equal to n.
What does ! mean in the formulas?
The symbol ! represents factorial. For example:
5! = 5 × 4 × 3 × 2 × 1 = 120
What is the difference between nPr and nCr?
In nPr, order matters. In nCr, order does not matter.
Conclusion
The Permutation and Combination Calculator provides a quick and convenient way to calculate nPr and nCr without manually performing complicated factorial calculations. Enter your values of n and r to get accurate results instantly.