If the letters of the word ‘SIPRON’ are arranged in all possible ways and the words thus formed
are arranged as in dictionary order. Find the rank of the word ‘PRISON’.

The letters of the word ‘SIPRON’ in dictionary order is
I         N            O         P            R        S
The number of words which begin with I = ⁵P₅ = 120
The number of words which begin with N = ⁵P₅ = 120
The number of words which begin with O = ⁵P₅ = 120

The number of words which begin with PI = ⁴P₄ = 24
The number of words which begin with PN = ⁴P₄ = 24
The number of words which begin with PO = ⁴P₄ = 24
The number of words which begin with PRIN = ²P₂= 2
The number of words which begin with PRIO = ²P₂= 2
The number of words which begin with PRISNO =¹P₁=1
The next word is PRISON =1
Rank of the word = 438