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Combination & Permutation Calculator
Calculate combinations C(n,r) and permutations P(n,r) instantly. Find how many ways to choose or arrange items from a set.
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Key Features — Combination & Permutation Calculator
Combination C(n,r) — order does not matter
Permutation P(n,r) — order matters
Handles large values using logarithms
Clear explanation of the difference
Ratio of permutations to combinations
Why Use This Tool — Combination & Permutation Calculator
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Frequently Asked Questions — Combination & Permutation Calculator
What is the difference between combination and permutation?
A combination counts the number of ways to choose r items from n where order doesn't matter: C(n,r) = n! / (r!(n-r)!). A permutation counts arrangements where order matters: P(n,r) = n! / (n-r)!. Choosing a 3-person committee from 10 is a combination (150). Ranking 1st, 2nd, 3rd in a race is a permutation (720).
When do I use combinations?
Use combinations when the order of selection does not matter: choosing lottery numbers, selecting a team from candidates, picking questions from a test, dealing cards. Use permutations when order matters: race placements, creating a password, arranging books on a shelf, scheduling events.
How do you calculate C(52,5) for poker hands?
C(52,5) = 52! / (5! × 47!) = 2,598,960. There are about 2.6 million distinct 5-card poker hands from a standard deck. Of these, only 4 are royal flushes, giving a royal flush probability of 4 / 2,598,960 ≈ 0.000154%.