Calculate nPr and nCr values for combinatorics problems.
Input Parameters
Calculation Results
120
Combinations (nCr)
Results showing different ways to select items.
Permutations (nPr)720
Difference Ratio3!
A
B
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D
E
F
G
H
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Picking 3 items out of 10
About this calculator
Quick Reference
OrderednPr (Permutation)
UnorderednCr (Combination)
n!n × (n-1) × ... × 1
0!Always equals 1
Science of Counting
Combinatorics is the branch of mathematics focusing on counting, arrangement, and selective combinations. A Permutation (nPr) is an ordered arrangement where sequence matters. A Combination (nCr) is a selection where order does NOT matter.
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Pro Tips
Use Permutations for arrangements, codes, or rankings (Order Matters).
Use Combinations for groups, teams, or sets (Order Doesn't Matter).
r must be less than or equal to n.
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Fun Facts
"The number of ways to shuffle a standard 52-card deck is 52! (approx 8 × 10⁶⁷)."
"Pascal's Triangle is essentially a geometric representation of all combinations (nCr)."
"The term 'combinatorics' was first used by Gottfried Leibniz in 1666."
