How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?

There are 8 different letters in the word EQUATION. 
The first place can be filled in 8 ways.
Second place can be filled by any one of the remaining 7 letters. So, second place can be filled in 7 ways
Third place can be filled by any one of the remaining 6 letters. So, third place can be filled in 6 ways
So, on continuing, number of ways of filling fourth place in 5 ways , fifth place in 4 ways, six place in 3 ways, seventh place in 2 ways, eighth place in 1 way.
Therefore, the number of words that can be formed using all the letters of the word EQUATION, using each letter exactly once is $8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=8!$

Alternative Method:
There are 8 different letters in the word EQUATION. 
 Therefore, the number of words that can be formed using all the letters of the word EQUATION, using each letter exactly once, is the number of permutations of 8 different objects taken 8 at a time, which is  ${}^8{P}_8=8!$
Thus, required number of words that can be formed = 8! = 40320