Combinatorics question about the four-letter sequence "GRIT"

[RM86Z]

Homework Statement

Given the letters in "FULBRIGHT" how many contain the four-letter sequence "GRIT".

Relevant Equations

6 x 5!

Question: "A total of 9! = 362880 different nine-letter ‘‘words’’ can be produced by rearranging the letters in FULBRIGHT. Of these, how many contain the four-letter sequence GRIT?"

Solution: There are six ways of getting the word "GRIT" with five letters left over giving 6 x 5! = 720 possibilities.

There is no answer in my book so just wanted to verify whether my solution is correct or not.

 

[PeroK]

Yes, you can consider GRIT as a single letter X. So $6!$

 

[RM86Z]

Thank you I didn't think of it that way but that does make sense!