C(12,5,2) = 9

Method of Construction: random greedy covering

 1  2  4  7  9 
 1  3  4  6 12 
 1  3  7 10 11 
 1  5  6  8 12 
 2  3  5  7  8 
 2  6 10 11 12 
 3  6  7  9 12 
 4  5  8 10 11 
 5  8  9 10 11