One simple way that may be a bit wasteful as it calculate more combinations than necessary and remove redundant ones:
Concatenate your 3 arrays and use nchoosek to pick all combinations of 4 elements from that concatenation. Remove duplicate combinations using unique (with the 'rows' option).
With only ten elements it's near instananeous anyway. With moderately more elements, nchoosek will take too long and generate too many combinations, so a different method will have to be used.
