Question

If the permutations of a, b, c, d, e taken all together be written down in alphabetical order as in dictionary and numbered, find the rank of the permutation debac.

Answer 1

Given,

The letters a, b, c, d, and e. 

Arranging the permutations of the letters a, b, c, d, and e in a dictionary : 

To find : Rank of word debac in dictionary. 

First comes, 

Words starting from letter a = 4! = 24 

Words starting from letter b = 4! = 24 

Words starting from letter c = 4! = 24 

Words starting from letter d : 

Words starting from da = 3! = 6 

Words starting from db = 3! = 6 

Words starting from dc = 3! = 6 

Words starting from dea = 2! = 4

Words starting from deb : 

debac = 1 

Rank of the word debac = 24 + 24 + 24 + 6 + 6 + 6 + 4 + 1 

= 95 

Hence, 

The rank of the word debc in arranging the letters a, b, c, d, and e in a dictionary among its permutations is 95.