Question on # of possible rearrangements given conditions

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To find the number of rearrangements of the letters in "INVESTIGATION" with the first letter as V and the last letter not being T, start with 12! for the total permutations. To address the last letter condition, calculate the permutations where T is the last letter, which is 11! since the first letter is fixed as V. Subtract this from the total permutations to find the valid arrangements. The final count will give the total number of valid rearrangements under the specified conditions.
thelannonmonk
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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.
 
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How many possibilities do you have for the last letter? And then before the last one?

ehild
 
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
 

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