The question is a little unclear, In particular, is the "or" inclusive or exclusive?
Also may letters be used more than once?
If letters can be used only once:
There are only 6 ways in which UVW can occur in a string of 8 so that the number of permutations with UVW will be 6 *5! and 7 ways the string ST can occur so that there are 7*6! ways for ST,
Then you need to decide what to do about strings in which BOTH occur.