Only the digit 4 can appear twice, but not twice in
a row, so the only ones with two 4's are these 3:

414, 424, and 434 

The rest have 3 different digits:

There are 4 ways to select the first digit.
For each of those, there are 3 remaining digits
to place for the second digit,
Foe each of the ways to place the first 2 digits, 
there are 2 ways to place the last digit.

So that's 4*3*2 or 24 ways.

So that's a total of 3 + 24 or 27 ways.

Checking:

 1. 123
 2. 124
 3. 132
 4. 134
 5. 142
 6. 143
 7. 213
 8. 214
 9. 231
10. 234
11. 241
12. 243
13. 312
14. 314
15. 321
16. 324
17. 341
18. 342
19. 412
20. 413
21. 414
22. 421
23. 423
24. 424
25. 431
26. 432
27. 434

Edwin