Question

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

• A. 38320
• B. 39320
• C. 40320
• D. 18400
• E. None of these

Answer 1

The correct option is C 40320

The word EQUATION has exactly 8 letters which are all different.
$\therefore$ Number of words that can be formed = number of permutations of 8 letters taken all at a time
$=P(8,8)=8!=8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=40320.$