(i) If the letters of the word EAMCET are permuted in all possible ways and if the words thus formed are arranged in the dictionary order, find the rank of the word EAMCET.

ii) If the letters of the word AJANTA are permuted
in all possible ways and the word thus
formed are arranged in dictionary order. Find
the rank of the words
(i) AJANTA
(ii) JANATA

Sol: The alphabetical words of the letters of the given word is A, C, E, E, M, T

∴ Rank of the word EAMCET = 133

i) Given word AJANTA
Dictionary order - A,A,A,J,N,T
The no of words begin with AA--- –4! = 24
The no of words begin with AJAA-- –2! = 2
The no of words begin with AJANA = 1! = 1
The no of words begin with AJANTA=0! = 1
The rank of the word
AJANTA = 24 + 2 + 1 + 1 = 28

Sol : (ii) The no of words begin with A ----$\frac{5!}{2}=60$
The no.of words begin with JAA--- =3! = 6
The no.of words begin with JANA A=1!= 1
The no.of words begin with JANATA = 0! = 1
The Rank of the word JANATA
= 60 + 6 + 1 + 1 = 68