Permutation and Combination Calculator: Free Math Tool
Permutation & Combination Calculator
Calculate nPr (Permutations) and nCr (Combinations) instantly for any given total and selection size.
CALCULATION RESULTS
Permutation ($nPr$): 0
Combination ($nCr$): 0
What are Permutations and Combinations?
In mathematics and probability statistics, counting techniques are fundamental for analyzing possibilities. A **Permutation** ($nPr$) refers to the number of ways to arrange a subset of items where **order matters**. Conversely, a **Combination** ($nCr$) calculates selections where **order does not matter**. Our online calculator computes both values instantly.
Formulas
Using factorials, permutations and combinations are derived through precise algebraic formulas.
Core Formulas:
- Permutation: $nPr = \frac{n!}{(n - r)!}$
- Combination: $nCr = \frac{n!}{r!(n - r)!}$
- Permutation: $nPr = \frac{n!}{(n - r)!}$
- Combination: $nCr = \frac{n!}{r!(n - r)!}$
Frequently Asked Questions (FAQ)
Q: What is the main difference between nPr and nCr?
A: The key difference is sequence. If arranging items in a specific sequence (like a password or race finish order), use Permutation. If selecting a group where sequence is irrelevant (like a committee), use Combination.
A: The key difference is sequence. If arranging items in a specific sequence (like a password or race finish order), use Permutation. If selecting a group where sequence is irrelevant (like a committee), use Combination.
Q: Can r be greater than n?
A: No, the number of items selected ($r$) can never exceed the total available items ($n$).
A: No, the number of items selected ($r$) can never exceed the total available items ($n$).
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