How many permutations of the letters STUVWXZA contain the strings UVW or ST?

Question

I need an answer to this question ASAP!

Answer 1

I think total different permutations: P₆ + P₇ - P₅ = 5640

Answer 2

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.