Question 636129: Please help. Completely lost...
In how many ways can the letters in the word TRANSPORTATION be arranged if the first letter must be an A and the last letter must not be a T?
Would really appreciate it
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! 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
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