Find and return Binomial Coefficients (BCs) in a matrix up to N.

Version 1.2.0.0 (2.63 KB) by Bruce Raine
This function can return N choose K (K <= N) as well as a BC matrix up to N choose N.
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Updated 30 Dec 2011

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The function BINOMIND(N,K,SPEED) does not use loops (apart from a redundant check) or division nor indeed factorials to generate the Binomial Coefficients (BCs). It simply constructs the lower-triangular Pascal matrix and does a simple lookup to get the desired BC.

BINOMIND is much faster than NCHOOSEK at creating matrices of BCs if you set SPEED to TRUE and also has a basic integrity check to compare it with nchoosek. It can return 3 lots of data: comb,binTable, errorRate but you can just use it to find combinations by default.

Cite As

Bruce Raine (2026). Find and return Binomial Coefficients (BCs) in a matrix up to N. (https://www.mathworks.com/matlabcentral/fileexchange/34375-find-and-return-binomial-coefficients-bcs-in-a-matrix-up-to-n), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2011a
Compatible with any release
Platform Compatibility
Windows macOS Linux
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Version Published Release Notes
1.2.0.0

Fixed one bug in the 'if nargin' statement on line 43 and improved 'if k > n' error message on line 49.
1.1.0.0

I added more input parameter checking, an extra input parameter, SPEED as well as a warning message for COMB values above a predefined tolerance limit. I also improved the documentation of the function.
1.0.0.0