Rank in a Dictionary

The dictionary format means words are arranged in alphabetical order. Following illustrations will help you learn how to find the rank in the
dictionary.

EXAMPLE : If letters of the word are arranged as in dictionary, then find the rank of the following words.

`(i) INDIA quadquadquadquadquad(ii) UMANG `

`Solution. (i)` The letters in alphabetical order are `A, D, I, I, N`

The first word is `ADIIN`

Number of words beginning with `A= (4 ! )/(2!)= 12`
Number of words beginning with `D =(4 ! )/(2!)= 12`
Number of words beginning with `IA = 3 ! = 6`
Number of words beginning with` ID = 3 ! = 6`
Number of words beginning with `II = 3 ! = 6`
Number of words beginning with `INA= 2 ! = 2`
Number of words beginning with` INDA = 1 ! = 1`
Number of words beginning with `INDIA= 1`
.. Rank of the word `INDIA= 12 + 12 + 6 + 6 + 6 + 2 + 1 + 1 = 46`


(ii) The letters in alphabetical order are `A, G, M, N, U`
. . The first word is `AGMNU`
Number of words beginning with `A= 4! = 24`
Number of words beginning with `G = 4! = 24`
Number of words beginning with `M = 4 ! = 24`
Number of words beginning with `N = 4! = 24`
Number of words beginning with `UA = 3! = 6`
Number of words beginning with `UG = 3 ! = 6`
Number of words beginning with `UMAG = 1 ! = 1`
Number of words beginning with `UMANG = 1`
Rank of the word
UMANG `= 24 + 24 + 24 + 24 + 6 + 6 + 1 + 1`
`= 110`