If letters of the word are arranged as in dictionary, find the rank of the following words.(i) INDIA (ii) SURITI (ii) DOCOMO

Explanation

(i) The letter in alphabetical order are A,D,I,I,N
`therefore`The first word is ADIIN
Number of words beginning with `A=(4!)/(2!)=12`
Number of words beginning with `D=(4!)/(2!)=12`
Number of words beginning with IA=3!=6
Number of words beginning with ID=3!=6
Number of words beginning with II=3!=6
Number of words beginning with INA=2!=2
Number of words beginning with INDA=1!=1
Number of words beginning with INDIA=1
`therefore`Rank of the word INDIA
=12+12+6+6+6+2+1+1=46
The letters inn alphabetical order are I,I,R,S,T,U
`therefore`The first word is IIRSTU
Number of words beginning with I=5!=120
gt Number of words beginning with R=`(5!)/(2!)=60`
Number of words beginning with SI=4!=24
Number of words beginning with SR=`(4!)/(2!)=12`
Number of words beginning with ST`=(4!)/(2!)=12`
Number of words beginning with SUI=3!=6
Number of words beginning with SURI=1!=1
Number of words beginning with SURITI=1
`therefore`Rank of the word SURITI
=120+60+24+12+12+6+1+1=236