Question

If we permute 6 letters of the word 'SYSTEM', the number of permuted words with a vowel at the third
place are:​

Answer 1

Answer :

60 words are possible on permuting word 'SYSTEM' with the vowel fixed at third position.

Explanation:

In the above question we are supposed to count the number of permutation of the word keeping the vowel fixed at the 3rd position.

The word 'SYSTEM' has only one vowel in it, that is 'E' so keeping it fixed at 3rd position, we have two S which are identical,

Initially considering the two S as different, the number of permutation will be 5! but since the two S are identical we need to divide it by 2. So the total number of permutations will be    

                                    $= \frac{5!}{2} = 60\ words.$