# How many words, with or without meaning,

Question:

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

Solution:

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 ${ }^{8} \mathrm{P}_{8}=8 !$

Thus, required number of words that can be formed $=8 !=40320$