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Question

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'.


Solution

In a dictionary the words at each stage are arranged in alphabetical order. 

Starting with letter I, and arranging the other 5 letters, we obtain 5!=5×4×3×2×1=120

Then starting with R, and arranging the other five letters I,I, S, T, U in different ways, we obtain 5!2!=1202=60.

Number of words beginning with 5 is 5!2!, but one of these words is the word SURITI itself. 

So, we first find the number of words beginning with SI, SR, ST, SUI and SURI. 

Number of words starting with SI = 4! = 24 

Number of words starting with SR = 4!2!
= 12

= 120+60+24+2×12+6+2 

=180 + 56 

= 236 

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