Combinations and Permutations Calculator: Free Math Tool
Combinations & Permutations Calculator
Calculate combinations ($nCr$) and permutations ($nPr$) instantly by entering total items ($n$) and chosen items ($r$).
CALCULATION RESULTS
Combinations (nCr): 0
Permutations (nPr): 0
What are Combinations and Permutations?
In mathematics, a **Permutation** is an arrangement of items where **order matters**, whereas a **Combination** is a selection of items where **order does not matter**. Our online **Combinations and Permutations Calculator** computes both values quickly and accurately.
Formulas
The standard mathematical formulas for calculating $nPr$ and $nCr$ using factorials are:
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 permutation and combination?
A: The key difference is order. If the arrangement sequence matters (like a password or lock code), use permutations. If order is irrelevant (like picking a team of players), use combinations.
A: The key difference is order. If the arrangement sequence matters (like a password or lock code), use permutations. If order is irrelevant (like picking a team of players), use combinations.
Q: Can $r$ be greater than $n$?
A: No, the number of items chosen ($r$) cannot exceed the total number of items available ($n$).
A: No, the number of items chosen ($r$) cannot exceed the total number of items available ($n$).
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