Modifying Melody's result a little we have:
1 * * * 1*4*4*4 = 64 ways, but 4 possible positions for the 1, so 64*4 = 256 ways
1 1 * * 1*1*4*4 = 16 ways, but 6 possible combinations of the two 1's, so 16*6 = 96 ways
1 1 6 * 1*1*1*4 = 4 ways, but 6 possible positions for the 1's
and two possible remaining positions for the 6, so 4*6*2 = 48 ways
1, 1, 1, any 1*1*1*5 = 5 ways, but 4 possible positions for the three 1's, so 5*4 = 20 ways
total = 256 + 96 + 48 + 20 = 420 ways
Hence probability = 420/1296 → 35/108 ≈ 0.324
.