Question on # of possible rearrangements given conditions

[thelannonmonk]

1. How many ways are there to rearrange the letters of INVESTIGATION given that the first letter is a V and the last letter is not a T?

I get the first part, first letter being V cuts the # of combinations from 13! to 12!, but how do I handle the part about the last letter not being T? Most of what I have found online doesn't really relate to this particular issue.

 

[ehild]

How many possibilities do you have for the last letter? And then before the last one?

ehild

 

[Ray Vickson]

12! is the number of permutations in which we allow both T and non-T as the last letter. Can you count the number in which T *is* the last letter?

RGV