Rank of a word
# Word having distinct alphabets
In this we are going to find rank of a word with distinct alphabets.
In permutations we often come across questions on number of words formed using letters of the given word.Here we are calculating rank of a word i.e. the place of a specific word when words are arranged as arranged in dictionary.
Consider a word SUMIT in which there are 5 alphabets and all are distinct.
From letters of the word SUMIT , there would be 5! = 120 different meaningful and meaning less words can be formed.
From letters of the word SUMIT , there would be 5! = 120 different meaningful and meaning less words can be formed.
If these words are arranged alphabetically i.e. as arranged in dictionary then the word SUMIT comes at certain place i.e.rank of a word SUMIT.
Procedure:
3 5 2 1 4
S U M I T
Then starting from left i.e from letter S, count the numbers to the right side which are less than 3 i.e.number corresponds to letter S which is third in alphabetical order of the word SUMIT.
So there are two numbers less than 3 i.e. 1 and 2 so write 2 below S as shown.
3 5 2 1 4
S U M I T
2
In the same way for next alphabet U the corresponding number is 5. So there are three numbers less than 5 to the right of U i.e. 2,1 & 4.So write 3 below U and so on for other alphabets.
3 5 2 1 4
S U M I T
2 3 1 0 0
Now from rightmost end write factorials start from 0! in increasing order up to last alphabet.
3 5 2 1 4
S U M I T
2 3 1 0 0
4! 3! 2! 1! 0!
Now multiply corresponding factorial with number written above it to get some results.
3 5 2 1 4
S U M I T
2 3 1 0 0
* * * * *
4! 3! 2! 1! 0!
The multiplication will give following results
3 5 2 1 4
S U M I T
2 3 1 0 0
* * * * *
4! 3! 2! 1! 0!
48 18 2 0 0
Now add numbers 48 + 18 + 2 + 0 + 0 = 68 .Add one to this addition to get a total of 69.
Rank of word SUMIT is 69.
