Rank of a Word: Permu-Combi Help

[Mr.IITIAN007]

Hey guys ! Is there any shortcut to find the rank of a particular word ??
If there is any, then what is it?

 

[cristo]

What do you mean by the rank of a word?

 

[Mr.IITIAN007]

Rank of a word means at which position it is written in the dictionary.

Rank of a word is nothing but the arrangement of the given letters of the word in dictionary..order n finding after how many words which r possible by these letters our favourable word occurs...let me xplain wisd a xample..


take the xample of the word "MASTER"

ARRANGE THESE LETTERS IN DICTIONARY ORDER...A,E,M,R,S,T

THEN THE NO OF WORDS BEGIN WITH A=5 FACTORIAL
"" "" "" E=5 """
" "" "" MAE=3 ''' "
"" "" MAR=3 "" "
"" """ MASE=2 " ""
" "" MASR=2 ""
" "" MASTER=1
=ADDIN THEM WILL GET 257 WHICH IS THE RANK OF MASTER...

CONCLUSION...OUR WORD MASTER OCCUR AS 257th WORD WHEN ARRANGED ACC TO DIC...WHICH MEANS 256 WORDS R POSSIBLE WID THESE LETTERS BEFORE THE WORD MASTER...

But this method is too lengthy and becomes even longer when the word is longer and has same letters more than once.

For example if the letters of the word 'SURITI' are written in all possible orders and these words are written out in a dictionary ,then the rank of the word is 236.Similarly the rank of the word 'RANDOM' is 614.

 

[Werg22]

You mean to say that if we were to list all possible arrangements of 6 numbers in increasing value order, is there a quick way to find the rank of one of these arrangements?

 

[Mr.IITIAN007]

Yes you can say that.

 

[Werg22]

Well, I don't believe there is any kind of short cut.

 

[Mr.IITIAN007]

But some of my friends solve this type of question within seconds.They seem to have a particular kind of trick.Well,they don't tell me.

 

[Werg22]

Hummm. I'll put my mind into it, I'll get back at you.

 

[Werg22]

Well I can't think of anything expect the obvious... if

Master = 315624

then the rank is given to us by (3 - 1)*5! + (1-1)*4! + (3 -1)*3! + (3 - 1)*2! + (1-1)*1! + (1 - 1)*0! = 268

In which the number x in (x - 1)*n! is the rank of the number in respect to the numbers on its right in 315624. I believe your 247 is wrong...

 

[Mr.IITIAN007]

O.K.Thats great man.But what is 'Master = 315624'.

 

[Werg22]

Well, all I did was to assign to each letter a number in respect to the alphabet. A is the first letter out of the 6, so I gave it 1 and etc. It really dosen't matter, all the information you need is the relative ranking of a digit in respect to the others. Working with numbers is easier than letters for me though, I have to recite the alphabet all over every time I want to check which letter comes first!

 

[sureshg9]

Hello Werg,

I did not understand "then the rank is given to us by (3 - 1)*5! + (1-1)*4! + (3 -1)*3! + (3 - 1)*2! + (1-1)*1! + (1 - 1)*0! = 268"

"x in (x - 1)*n! is the rank of the number in respect to the numbers on its right in 315624"
what does this mean. Right...does it mean no. of digits to X's right side?

Please help me in understanding this. I desperately need to learn this short cut.

 

[HallsofIvy]

It is not that difficult to calculate how many combinations of, say, 6 letters there are and where in that list a particular order comes, but that does not answer the question about "dictionary rank". For example, if I were to argue that there are $26^3= 17576$ three letter combinations of the 26 letters of the alphabet, and that "and" would come, in alphabetical order, at position 14*26+ 4= 368 in that list, that would NOT tell me where in the dictionary "and" comes. For one thing, that includes combinations of letters, like "agf", that are not words. For another, a dictionary would include words longer that three letters before "and".