See this question in this site. The question was about a shortcut method for finding the rank of the word COCHIN. N. F. Taussig and true blue anil have provided good explanations. Finally, it was said that there is no shortcut method for finding rank if the word is having repeated characters.
True blue anil has given an example for the word 'SUCCESS' and explained why there is no shortcut method work for this. Following is from his explanation.
Let us illustrate taking the word SUCCESS
Letters fixed from the left will be enclosed in [...], the ...
for computing permutaions of the remaining letters.
Starting turn by turn with the lowest ranking letter(s), we get
[C...]:6!/3!=120
[E...]:6!/3!2!=60
[SC..]:5!/2!=60
[SE..]:5!/2!2!=30
[SU..]:1[ The remainig letters, CCESS
are already in lexicographic order.
Why the "shortcut method" doesn't work here is because, for example, permutations starting with SC
aren't the same as permutations starting with SE, and we can't foretell this.
But, recently came across this online tool from careerbless.com which finds dictionary rank using shortcut method. It claims that it takes care of repeating and non-repeating letters.
Using the above tool, I have calculated rank of COCHIN and and rank was obtained as $97$. Also calculated the rank of success and obtained as $331$
yes, for repeating letters, the answer varies. As per the explanation quoted by 'True blue anil, rank must be $120+60+60+30+1=271$ . (quora.com also gives answer as $271$). But the tool I mentioned gives $331$ as the rank.
But, I feel that $331$ is the right answer as obtained in the tool because, the explanation by 'True blue anil' misses the $60$ permutations starting with 'SS'. If this is right, then the general method works.
Can anyone explains me whether I am right here and the shortcut method given in the tool can be used reliably? or still, I missed out something in my analysis? (note: I cannot copy the output of the tool as it is a video)
Suppose, this tool is reliable, then I would like to know the reason for its logic also because I per the suggestions obtained in the referred question, repeated characters will not work in general.
Obviously, if this shortcut method works, I want to use it to save time for my exams. My question may be seen in that context. Thanks.
EDIT: Noted one more variance.
Calculate rank of the word 'MOHAN' (question taken from this book)
Answer given in the book is $63.$
The tool I referred gives $69$ as the rank
Regarding $SUCCESS$, as you point out, there was an oversight in my previous answer as [SS..] was missed out, (now corrected), the correct answer is $331$
Regarding MOHAN, the link you cite has missed out [MN..] by oversight, if corrected, answer is $69$
Since you give no link to the "tool", it isn't possible to comment on its correctness.
The tool linked in your comment works, as when letters are repeated, it takes into account variations in permutations due to such repetitions.
The basic idea is to count how many words are formed before the $S$ becomes the first word, then how many words from the remaining letters are formed before the required $U$ turns up, and so on.