Combinations, n choose k

This function finds the combinations of n choose k.

Description

The combination function seems to be missing from MATLAB so this rendition fills the gap.

MYCOMBNK returns combinatorial of n choose k i.e all unique combinations of n elements taken k at a time.

EX: >> mycombnk(6,2)
 ans = 15

• MATLAB release: MATLAB 7.12 (2011a)

[Jan Simon]

Have you seen the built-in function NCHOOSEK?! It uses a more stable method than your function, because factorial(n) cannot be represented exactly as DOUBLE for n>=19.

[mklcst mklcst]

I really don't understand the purpose of this function.
It's simply a binomial coefficient, it would be better to create the possible combination with and w/o replacement.

[Bruce Raine]

Actually I tested my function against NCHOOSEK and discovered it was fine until n=54 and then it differed only by a minuscule fraction of the mantissa. It seems stable above that too and incidentally NCHOOSEK becomes unstable at n=54. As for the FACTORIAL function it works well enough and in fact worked up to n=150 inside my function. I can send you my testbed code which shows how well the MYCOMBNK performs against MW function.

[Bruce Raine]

The binomial coefficient is arguably the most important coefficient in probability. It is the basic building block of probability distribution functions, for example, the Binomial distribution and the Hypergeometric distribution. Indeed, the binomial coefficient sits at the heart ot Probabilistic Combinatorics.

As for replacement and w/o replacement, these two concepts depend on what kind of probability you intend to calculate and not the binomial coefficient. I have written several other functions making use of the binomial coefficient which I may upload soon.