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version 1.2.1 (3.75 KB) by Jan
Fast and accurate N over K


Updated 22 Feb 2022

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N over K
A fast and stable computation of: n! / (k! * (n-k)!)
This is the number of combinations, if k elements are chosen out of n without
repetitions and order.
[c, OF] = NoverK(n, k)
n, k: Scalars with real integer values, floating point or integer types.
c: Result as same type as the inputs.
OF: Logical flag, true on overflow.
- Alternatives:
prod(((n-k+1):n) ./ (1:k)) 3 times slower, less accurate
nchoosek(n, k) 20 times slower, less accurate:
nchoosek(61, 17) 536830054536826 (14 valid digits only)
NoverK(61, 17) 536830054536825
The accuracy and overflow handling was the main reason to write this function.
Tested: Matlab 2009a (no U/INT64!), 2015b(32/64), 2016b, 2018b, Win10

Cite As

Jan (2022). NoverK (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2018b
Compatible with R2009b and later releases
Platform Compatibility
Windows macOS Linux

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