Try this out (adapt the values to your needs):
m = 10;
n = 3;
pos = randperm(m*n,m);
M = zeros(m,n);
M(pos) = 1;
M =
0 0 0
1 1 0
0 1 1
0 0 0
1 0 0
0 0 0
0 0 0
1 0 1
0 1 1
0 0 1
M has the ones randomly distributed.
