Question 636129
The first letter must be an A. So the word looks like


A _ _ _ _ _ _ ...


So you're really arranging 14-1 = 13 letters in 13 slots


The last letter must not be a T. So you have 13-1 = 12 choices for the last slot


The other slots go like this:


You have 13-1 = 12 choices for the second slot (after you choose a letter that is not T for the last slot)


You have 12-1 = 11 choices for the third slot


You have 11-1 = 10 choices for the fourth slot


etc

etc


all the way down to


You have 2 choices for the second to last slot


You have 1 choice for the last slot


Multiply all these choices out:


12*12*11*10*9*8*7*6*5*4*3*2*1 = 5748019200


Now divide by 2!*2!*3! = 4*4*6 = 96 to get 5748019200/96 = 59,875,200


This is to correct for the duplicates


So there are 59,875,200 ways to arrange the letters.



Note: if you are entering this into an online system, then chances are that you'll have to enter the number WITHOUT commas