If all the words which can be made by using some letters are arranged in dictionary in alphabetical order then position at which a particular word appears, is known as its rank. For example, 24 words can be made by using letters of the word “RANK” without repetition. Now to calculate position of the word “RANK” we arrange the words in alphabetical order.

A –– –– –– 3! words 

K –– –– –– 3! words 

N –– –– –– 3! words 

R A K N 1 word

R A N K 1 word

Hence the position of the word RANK is:  3! +  3! + 3! + 1 + 1 = 20.

Take one more example. 

Example: Find the rank of the word INDIA, if all the words that can be formed using letters of the word INDIA are arranged in alphabetical order.
Solution: Let us arrange the words in alphabetical order.

A – – – –  4!/2! words

D – – – –  4!/2! words

I A – – –   3! words

I D – – –   3! words

I I – – –    3! words

I N A – –  2! words

I N D A I  1 word

I N D I A  1 word

Hence rank of the word INDIA = 12 + 12 + 6 + 6 + 6 + 2 + 1 + 1  =  46.

Example 01: Find the rank of the word GOOGLE if all the words that can be formed by permuting letters of this word without repetition are arranged in the dictionary in alphabetical order.