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.

Explanation

In a dictionary the words at each stage are arranged in alphabetical order. We must consider the words beginning with I,R,S,T,U in order.
`therefore ` Number of words starting with I=5! =120
Number of words starting with `R=(5!)/(2!)=60`
Number of words beginning with S is `(5!)/(2!)`, but one of these words is the word SURITI, So, we first find the number of words beginning with SI,SR,ST
Number of words starting with `SI=4!""=24`
Number of words starting with SR=`(4!)/(2!)=12`
Number of words starting with `ST=(4!)/(2!)=12`
Now, the words beginning with SU must follow. There are `(4!)/(2!)=12` words beginning with SU, but one of these words is the word SURITI, Number of words starting with SUI=3!=6. The first word beginning with SUR is SURIIT and the next word is SURITI.
`therefore ` Rank of SURITI `=120+60+24+2xx12+6+2=236`