How can I generate all possible combinations from multiple sets of nchoosek?

Basically, I want to run combntns on multiple sets. Given multiple vectors and knowing how many elements to choose from each vector, can I generate all possible combinations? I suppose it can be done with for loops, but I am hoping for something more elegant.

Example

If

n1 = [1,2,3]; k1 = 1;
n2 = [4,5,6]; k2 = 2;

then

c = [1 4 5
     1 4 6
     1 5 6
     2 4 5
     2 4 6
     2 5 6
     3 4 5
     3 4 6
     3 5 6]

Answer 1

[Matthew Eicholtz]

In case anyone else ever stumbles upon this question...I figured out how to solve my problem. Use a combination of nchoosek and combvec:

c1 = nchoosek(n1,k1);
c2 = nchoosek(n2,k2);
c = combvec(c1',c2')';

To order the rows in the same way as shown in the question, use:

csorted = sortrows(c);