how to get combination of matrix columns

I would like to get all the possible combination between two column of a matrix.

supoose my matrix is

matrix =

          [1 1 1 1
           1 0 0 0
           1 0 1 0 
           0 1 1 0]
combination between column 1 and column 4 can be

column 1 and column 4

column 1 and column 2 and column 4

column 1 and column 3 and column 4

column 1 and column 2 and column 3 and column 4

so column 1 and column 4 should be present in every case.

[I want this using for loop]

Answer 1

[Guillaume]

Why are 1 and 4 singled out specifically?

As this sounds like homework, I'm not giving you the code, but you can simply:

1. use a for loop to iterate between 0 and the number of column - number of column singled out, call the index k.
2. use nchoosek to select all combinations of k elements out of the index of the remaining columns
3. use the indices returned by nchoosek plus your singled out columns to extract the column combinations.