For Hamming distance 10 means 10 bit should be different from 15 bit. So there are 15! / 10! * 5! ways to chose 10 bit from 15 bit.

```
15 X 14 X 13 X 12 X 11
------------------------------- = 3003
5 X 4 X 3 X 2
```

And 2 value possible for each bit. So total number for Hamming distance 10 = 3003 X 2 = 6006