the letters of the WIFE are arranged in all possible ways and sorted in dictionary manner.What is the position of the word WIFE in this arrangement?

Dear Student,

Letters of the word WIFE in dictionary manner = E . F , I , W

$\Rightarrow$Words starting with letter E: 
First letter of the word is taken by E
Second letter can be taken by remaining 3 letters
Third letter can be taken by remaining 2 letters
Fourth letter can be taken by remaining 1 letter

Hence, total number of words starting with E = 1 x 3 x 2 x 1 = 6

Similarly words starting with F and I will be 6 each

Now,
$\Rightarrow$Words starting with letter W: 
First letter of the word is taken by W
Second letter is taken by E
Third letter can be taken by remaining 2 letters
Fourth letter can be taken by remaining 1 letter

Hence, total number of words starting with W and Second letter as E = 1 x 1 x 2 x 1 = 2 

First letter of the word is taken by W
Second Letter is taken by F 
Third letter can be taken by remaining 2 letters
Fourth letter can be taken by remaining 1 letter

Hence, total number of words starting with W and Second letter as F = 1 x 1 x 2 x 1 = 2 

First letter of the word is taken by W
Second Letter is taken by I
Third letter is taken by E
Fourth letter can be taken by remaining 1 letter
Hence, total number of words starting with W and Second letter as I and third letter as E = 1 x 1 x 1 x 1 = 1
 
First letter of the word is taken by W
Second Letter is taken by I
Third letter is taken by F
Fourth letter can be taken by remaining 1 letter i.e. E

Hence we arrive at word WIFE

Now words before WIFE are 6 + 6 + 6 + 2 + 2 + 1 = 23

Hence rank of word WIFE is 24th

Regards