The letters of the word ‘SURITI’ are written in all possible order

1.	The letters of the word ‘SURITI’ are written in all possible orders, and these words are written out as in a dictionary. Find the rank of the word ‘SURITI’.
Answer» Given, The word SURITI. Arranging the permutations of the letters of the word SURITI in a dictionary : To find : Rank of word SURITI in dictionary. First comes, words starting with letter I = 5! = 120 Words starting from letter R = 5!/2! = 60 Words starting from SI = 4! = 24 (4 letters no repetation) Words starting from SR = 4!/2! = 12 (4 letters, one repetation of I) Words starting from ST = 4!/2! = 12 (4 letters, one repetation of I) Words starting from SUI = 3! = 6 (3 letters no repetation) Words starting from SUR; SURIIT = 1 SURITI = 1 Rank of the word SURITI = 120 + 60 + 24 + 12 + 12 + 6 + 1 + 1 = 236 Hence, The rank of the word SURITI in arranging the letters of SURITI in a dictionary among its permutations is 236.

The letters of the word ‘SURITI’ are written in all possible orders, and these words are written out as in a dictionary. Find the rank of the word ‘SURITI’.

Answer»

Given,

The word SURITI.

Arranging the permutations of the letters of the word SURITI in a dictionary :

To find : Rank of word SURITI in dictionary.

First comes, words starting with letter I = 5! = 120

Words starting from letter R = 5!/2! = 60

Words starting from SI = 4! = 24 (4 letters no repetation)

Words starting from SR = 4!/2! = 12 (4 letters, one repetation of I)

Words starting from ST = 4!/2! = 12 (4 letters, one repetation of I)

Words starting from SUI = 3! = 6 (3 letters no repetation)

Words starting from SUR; SURIIT = 1

SURITI = 1

Rank of the word SURITI = 120 + 60 + 24 + 12 + 12 + 6 + 1 + 1

= 236

Hence,

The rank of the word SURITI in arranging the letters of SURITI in a dictionary among its permutations is 236.