If the letters of the word PRISON are permuted in all possible ways and the words thus formed are arranged in dictionary order, find the rank of the word. PRISON

Explanation

The letters of the given word in dictionary order are
I N O P R S
In the dictionary order, first all the words that begin with I come. If I occupies the first place then the remaining 5 places can be filled with the remaining 5 letters in 5! ways. Thus, there are 5! number of words that begin with I. On proceeding like this we get
`I rarr5!` ways
`N rarr 5!` ways
`O rarr 5!` ways
`PI rarr 4!` ways
`PN rarr 4!` ways
`PO rarr 4!` ways
`PRIN rarr 2!` ways
`PRIO rarr 2!` ways
`PRISNO rarr 1` way
`PRISON rarr 1` way
Hence the rank of PRISON is
`3xx5! +3 xx4! +2 xx2!+ 1xx1`
=360+72+4+1+1=438.