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Dictionary Rank of a Word Calculator

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Overview

This tool calculates rank of a given word when all the letters of that word are written in all possible orders and arranged in alphabetical or dictionary order. It supports words with repeating letters and non-repeating letters.

It uses shortcut method for the calculation and explains the steps using animation. You can pause/continue the animation using pause/play buttons. Alternatively, animation can be skipped using stop button.

Example 1 (when the letters of the word are not repeating)

If all the letters of the word 'PRIME' are arranged in all possible ways and written out in alphabetical(dictionary) order, then find the rank of the given word.

Solution 1 (Using the Concepts of Permutations and Combinations)

The word 'PRIME' has $5$ letters in which no letters are repeating.
Number of words starting with E $=4!=24$
Number of words starting with I $=4!=24$
Number of words starting with M $=4!=24$
Number of words starting with PE $=3!=6$
Number of words starting with PI $=3!=6$
Number of words starting with PM $=3!=6$
Number of words starting with PRE $=2!=2$
Number of words starting with PRIE $=1!=1$
Next word is 'PRIME'.
Therefore, rank
$=24+24+24+6+6+6+2+1+1=94$

Solution 2 (Shortcut Method, Using This Tool)

Click here to find rank of the word 'PRIME' using this calculator.

Example 2 (when the letters of the word are repeating)

If all the letters of the word 'SECRET' are arranged in all possible ways and written out in alphabetical(dictionary) order, then find the rank of the given word.

Solution 1 (Using the Concepts of Permutations and Combinations)

The word 'SECRET' has $6$ letters in which there are two 'E'.
Number of words starting with C $=\dfrac{5!}{2!}=60$
Number of words starting with E $=5!=120$
Number of words starting with R $=\dfrac{5!}{2!}=60$
Number of words starting with SC $=\dfrac{4!}{2!}=12$
Number of words starting with SECE $=2!=2$
Next word is 'SECRET'.
Therefore, rank
$=60+120+60+12+2+1=255$

Solution 2 (Shortcut Method)

Click here to find rank of the word 'SECRET' using this calculator.

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