Ok, I need some help here, I dont know how the answers got this answer, so I wonder if any of you can help.

The letters of the word TRIANGLE are to be formed into words (not necessarily making any sense) without repeating any letter twice. How many eight-letter words can be formed if the words must not have the I, A and N adjacent (this goes for I,A,N AND N,A,I AND A,N,I ect...)

I can understand $\displaystyle 8!-6*3!$ yet the answers have $\displaystyle 8!-6!*3!$

Are the answers wrong or am I? Why 6!?

If this is in the wroing forum you can move it!