Question on # of possible rearrangements given conditions

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The discussion focuses on calculating the number of rearrangements of the letters in "INVESTIGATION" with the constraints that the first letter is 'V' and the last letter is not 'T'. The initial calculation reduces the total permutations from 13! to 12! due to the fixed first letter. To account for the last letter not being 'T', participants suggest calculating the total permutations with 'T' as the last letter and subtracting this from the total permutations.

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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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