how many permutation of the letters PQRSTUVWX contain the string VWX or WX

Question

I know how to calculate each task like the following 7! + 8! but I am not sure how to subtract the overlapping part usually, it will the (or) parts is between distinct string, but in this example, they share 2 letters how do I solve this?

Answer 1

If repetition is not allowed and order isn't important, then you have $6!$ ways to do the string.

But note that, if you have the events

$E_1$: The string contains WX & $E_2$: The string contains VWX

We have that $E_1 \cup E_2= E_1$ So, I think, it is enough to say in your title that '... contain the string WX'