Permutation and combination

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             Permutation and combination
   
  
   


DICTIONARY PROBLEM :-
      (Shortcut method )
Rank:

• Q.1. If the letters of the word MOTHER written in all possible orders and arranged as in a dictionary, 
 the rank of MOTHER will be_ __

• Q.2. If the letters of the word SACHIN written in all possible orders and arranged as in a dictionary,
 then the rank of SACHIN will be__

•SOLUTION.1  
  the word :        MOTHER , 
 having  six distinct  alphabet letter.
•Arrange like ,                                                                                    M         O         T         H         E       R
•1ststep: Rank alphabet alphabetical order.                           3          4         6          2         1         5
•2ndstep:  write this way.                                                               5!        4!        3!         2!       1!        0!
•3rdstep: smaller than the  selective alphabet.                        2         2         3          1          0        0 
•4thstep: multiply and sum .   
   
  Rank:=(2*5!+2*4!+3*3!+1*2!+0*1!+0*0!)+1
                           = 309 ,

•Rank:= 309 th rank .

•  SOLUTION:  2.    
    the word ,  SACHIN 
                   A  C  H I  N  S    (six letter),
arrage alphabetical order ,
Similarly we done this way,
    Rank = (  5*5!+0*4!+0*3!+0*2!+0*1!)+1
 Rank:=  601 th. ( Ans )
Location: India India

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