Rank Of A Word In A Dictionary - Practice Questions & MCQ

A common type of problem asked in many examinations is to find the 'rank' of a given word in a dictionary. What this means is that you are supposed to find the position of that word when all permutations of the word are written in alphabetical order.

Rank of a word - without repetition of letters

Example:

Find the rank of a word MATHS in a dictionary made using its letters

Step 1: Write down the letters in alphabetical order. 

             The order will be A, H, M, S, T.

Step 2: Find the number of words that start with a superior letter. 

   Any word starting from A will be above MATHS. So, if we fix A at the first position, we have 4! = 24 words. (number of    ways arranging H, M, S, T).

              Similarly, there will be 24 words that will start with H. 

              Number of words start with MAH is 2! = 2

              Number of words start with MAS is 2! = 2

              Number of words start with MATHS is 1! = 1

Therefore, the overall rank of the word MATHS is 24 + 24 + 2 + 2 + 1 = 53

Rank of a word - with repetition of letters

Example

Find the rank of a word INDIA in a dictionary made using its letters

Write down the letters in alphabetical order, the order will be A, D, I, I, N.

• Number of words start with A is 4!/2! = 12 (We are dividing by 2! because I is repeating itself)
• Number of words start with D is 4!/2! = 12
• Number of words start with IA is 3! = 6 (number of ways arranging I, D, N)
• Number of words start with ID is 3! = 6 
• Number of words start with II is 3! = 6 
• Number of words start with INA is 2! = 2
• Number of words start with INDA is 1! = 1  
• Number of words start with INDIA is 1! = 1  

Therefore, the overall rank of the word INDIA is 12 + 12 + 6 + 6 + 6 + 2 + 1 + 1= 46