Combination Calculator

For multiset permutations, e.g. MISSISSIPPI is 1, 4, 4, 2 (M, I, S, P). They should add up to n.
Number of arrangements
2,598,960
Combinations and Permutations Calculator
Exact count
2598960
Formula
C(52,5) = 52! / (5! x 47!)
Combinations nCr
2,598,960
Permutations nPr
311,875,200
Combinations with repetition
3,819,816
Permutations with repetition (n^k)
380,204,032
Probability of one specific arrangement
0
Odds
1 in 2598960
Worked out from NIST Digital Library of Mathematical Functions, 26.3 Lattice Paths: Binomial Coefficients and 26.4 Multinomial Coefficients and 1 other source.

How this is worked out

2 steps
  1. Order does not matter and items are not reused, so this is the binomial coefficient.
  2. C(52,5) = 52! / (5! x 47!) = 2598960

Results are general information, not financial, tax, legal, medical or engineering advice.