Shortcut Trick to find out rank of word or word of any rank with repeat

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 Math Trick to find out rank of any word ,Math Trick to find out word of any rank with repeating letter.

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We know very large number of students facing problem  to find out rank of any word or word of any rank when letters are repeating, so here is the solution very easy to use just learn and deploy. 

Example : 

If you understand our tutorial for nor non-repeating , then its very easy for you.

See -  Rank  of word  INDIA in dictionary ?

So start same as we done previously. just start-

Step1 - do numbering over all letters.

4   3     2    1     0        <==   diraction
I    N    D     I     A


Step 2 :

Move left to right and put n for each letter .

4   3     2    1     0       <==   diraction
I    N    D     I     A
n   n     n     n    n       ==>   diraction

n defines as number of letter smaller than that letter in right hand side. ( refer previous post for better understanding ).

Note- an additional k factor to be added here for repeating letters .
1)  if letter repeat in right side then k= 1/( r! ) where r is number of that letter
2)   otherwise k=1 .

So in this case

1) For I ,  ( A , D )  is smaller in right hand side so n=2 , k=1/(2!) (I is repeating in right side and r=2)

2) For N , (A,D,I) smaller in right hand side so n=3 , k=1 (letter non-repeating in right side)

3) For D ,  (A) is smaller in right hand side so n=1 , k=1  (letter non-repeating in right side)

4) For I ,  (A) is smaller in right hand side so n=1 , k=0  ( no any letter repeating in right)

and so on .....

you can do this very fastly by manual work like

factorial      4      3     2     1     0       <==   diraction
word           I      N     D     I     A
n=>            2     3     1     1     0         ==>   diraction
k=>        1/(2!)   1      1     1     1

Now calculate ==>[ sum ( ( factorial ! )  x n x k)] + 1 (INDIA itself) ( ie. multiply column's but 1st row used as factorial)

So

Rank =  [( 4!) x 2 x 1/2! + ( 3!) x 3 x 1 + ( 2!) x 1 x 1 +  ( 1!) x 1 x 1] + 1 = 24 + 18 + 2 +1+ 1 = 46

Rank of word "INDIA" = 46

Hope you enjoyed this post , comment for any problem.

 

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