Case 1:  There are 0 solutions.
Case 2:  There is 1 solution:  RRGR.
Case 3:  There are 20 solutions.
Case 4:  There are 150 solutions.
Case 5:  There are 500 solutions.
Case 6:  There are 625 solutions.
Case 7:  There is 1 solution:  RGBO.
Case 8:  There are 0 solutions.
Case 9:  There is 1 solution:  ORGB.
Case 10:  There are 9 solutions.
Case 11:  There is 1 solution:  RRGG.
Case 12:  There is 1 solution:  BORG.