In order to be greater than 3000, the first digit must either be 3 or 4

Case 1. When the first digit is 3:
Then the rest of the digits must come from this list: 2, 2, 3, 3, 4, 4, 4, 4
Therefore we may choose any 3-digit sequence containing only 2's, 3's, & 4's
except we can't choose 222 or 333.  So there are 3*3*3 - 2 = 25 for case 1.

Case 2. When the first digit is 4:
Then the rest of the digits must come from this list: 2, 2, 3, 3, 3, 4, 4, 4
Therefore we may choose any 3-digit sequence containing only 2's, 3's, & 4's
except we can't choose 222.  So there are 3*3*3 - 1 = 26 for case 2.

Answer = 25+26 = 51

Edwin