How many words can be formed from the letters of the word ADROIT, which neither begin with T nor end in A ?
Here order of letters matters. Therefore, this is a case of permutation.
There are 6 letters. The followings are the positions of 5 letters "ADROIT": 123456
Since T cannot be placed in the first place and A in last place, 5 letters are accounted for rest of the five places.
Here is a little confusion: Whether the repetition of letter is allowed.
1. If repetition allowes: 4x6^5
2. If repetition is not allowed: 6! - 5! - 5! + 4! = 504
6! = total possibilities
5! = T at the first place
5! = A at the last place
4! = Repetation of "T at the first place while A at the last place" or "A at the last place while T at the first place"