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If letters of the word MAHARASHTRA are arranged in dictionary oreder then what is rank of the word MAHARASHTRA? Pl give solution Thanks

If letters of the word MAHARASHTRA are arranged in dictionary oreder then what is rank of the word MAHARASHTRA?


Pl give solution


Thanks

Grade:

2 Answers

shaswat roy
19 Points
10 years ago

MAHARASHTRA (1)

it is clear dat d words beginning wid A nd H will come before (1)

no. of words beginning wid A are 10!/(3!)(2!)(2!)=151200, no. of words beginning wid H are 151200/4=37800

now d 1st letter is M, 2nd letter is A let d 3rd letter b A :d no. of such words is 8!/(2!)(2!)(2!)=5040

1st is M,2nd is A, 3rd is H,4th is A let 5th b A :d no. of such words is 6!/2!=360

no. of words beginning wid MAHAH are 6!/2!=360, MAHARAA are 4!=24,MAHARAH are 4!=24,MAHARAR are 4!=24

no. of words beginning wid MAHARASA are 3!=6,MAHARASHA are 2!=2,MAHARASHR are 2!=2

thus we hav all dese words before MAHARASHTRA [ans=194842]

d main trick is to proceed from left 2 right nd keep changing d first letter wid a lower letter in d word till d 1st letter matches wid dat of d main word nd proceed similarly for d 2nd letter nd so on.

Pranav Sadavarte
19 Points
3 years ago
Words starting with A are 10!/3!2!2! i.e 151200 words Now starting with H are 10!/4!2! Only i.e 75600 words and not 37800 Now proceeding in same way as given in above solution we get rank of Maharashtra as 232464

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