Creating binary matrix with at least q ones on each row

I have a matrix which is intended to represent gender, so I want it to be roughly 0's and 1's. I am doing it as follows:

sex=round(rand(m,n));

The problems is that sometimes generates rows with only 0's or 1's. I want to change it so that it always contains at least q 1's and at most k 0's. Is there an easy way to do this?

Answer 1

[Walter Roberson]

   temp = [ones(m,q), zeros(m,k), round(rand(m,n-k-q))];

Now you can randomize the order within each row of temp

[~, idx] = sort( rand(m,n), 2);
sex = temp(sub2ind(size(temp), ndgrid(1:m,1:n), idx));

However: neither sex nor gender are binary. There are over a dozen intersex conditions; the wider field is Disorders of Sexual Development; and see http://www.joshuakennon.com/the-six-common-biological-sexes-in-humans/. There at least 19 catalogued genders; New York City recognizes 31 gender identities

[Josue Sandoval]

Very good answer, thanks!