Let me try

1) If 9 is the very left digit, then the second left digit has 6 possible numbers: 8,7,6,5,4,3; the third left also has 6 possibilities: 7,6,5,4,3,2,..., so the total numbers: 1x6x6x6x6

2) If 8 is the very left digit, the total numbers: 1X5x5x5x5

3) if 7 is the very left digit, the total numbers: 1x4x4x4x4

4) if 6 is the very left digit, the total numbers: 1x3x3x3x3

5) if 5, then: 1x2x2x2x2

6) if 4, then: 1x1x1x1x1

Then, add up.