Permutation Calculator (nPr)
Counts ordered arrangements, such as the finishing orders of a race or the possible codes for a lock.
Permutations
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Digits —
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The formula
nPr = n! ÷ (n − r)! with repeats: n^r
Results below 10²¹ are shown exactly. Larger ones are worked out through logarithms and shown in scientific notation, to a few significant figures.
What to watch out for
A “combination lock” is really a permutation with repeats, since 1-2-3 and 3-2-1 are different codes.
Frequently Asked Questions
How many ways can 3 of 10 people finish first, second and third?
720.
How many 4-digit codes are there?
10,000, with repeats allowed.
How many ways can a deck of 52 cards be ordered?
8.0658×10^67.