Question

Find the number of words formed (may be meaningless) by using all the letters of the word ‘EQUATION’, using each letter exactly once.

Answer 1

There are 8 alphabets in the word EQUATION.

Formula:

Number of permutations of n distinct objects among r different places, where repetition is not allowed, is

P(n,r) = n!/(n-r)! 

Therefore, a permutation of 8 different objects in 8 places is 

P(8,8) =  \(\frac{8!}{(8-8)!}\) = \(\frac{8!}{(0)!}\) = \(\frac{40320}{1}\) = 40320 

Hence there are 40320 words formed.