Calculating Combinations in Matlab and Octave

In Matlab and Octave, the nchoosek() function is used to compute combinations.

nchoosek(n,k)

Here, 'n' is the total number of elements, and 'k' represents the number of elements in each combination.

This function calculates the binomial coefficient, which is the number of ways to choose k elements from a set of n elements at a time.

Essentially, it takes a set of 'n' elements and outputs all possible combinations of these elements grouped by 'k'.

For example, to find out the number of ways to select 2 elements from a set of 3:

nchoosek(3,2)

ans=3

The nchoosek() function returns the total number of possible combinations.

To view a detailed list of combinations, you need to specify an array of elements as the first argument.

Let's define an array with three elements:

V=[1,2,3]

Now, I'll generate all possible combinations of 3 elements taken 2 at a time by passing this vector as the first argument and the number of elements to be grouped together as the second argument.

nchoosek(V, 2)

In this instance, the function outputs a matrix where each row is a possible combination of the three elements from the vector V, taken two at a time.

ans =

   1   2
   1   3
   2   3

Each combination is distinct, and the order of elements is irrelevant.

And so forth.