Only one.
There is no such formula since most of the possible permutations will not be words.
There are 9! permutations of the word 'insomnia.' That includes all combinations, whether they are or are not actual words.
39916800 permutations are possible for the word INFORMATION.
10! permutations of the word "Arithmetic" may be made.
There are 8! = 40320 permutations.
If you mean permutations of the letters in the word "obfuscation", the answer is 1,814,400.
There are 6! = 720 permutations.
There are 7 factorial, or 5040 permutations of the letters in the word NUMBERS.
There are 195 3-letter permutations.
There are 420.
There are 5040.