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

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.

Approved

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