How many arrangements, whether meaningful or not, can be created using all the letters of the word EQUATION, with each letter used exactly once?

There are 8 different letters in the word EQUATION. 
The first place can be filled = 8 ways.
Second place can be filled by any one of the remaining 7 letters. 
So, second place can be filled = 7 ways
Third place can be filled by any one of the remaining 6 letters. 
So, third place can be filled = 6 ways
Therefore, the number of words that can be formed using all the letters of the word EQUATION, using each letter exactly once = $8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=8!=\mathbf{40320}$