Question

The letters of the word ASHISH are permuted and are arranged in an alphabetical order as in an English dictionary. Then, the rank of the word ASHISH is __.

Answer 1

Let us arrange the letters of the word ASHISH in the alphabetical order.

AHHISS

In the dictionary, the words appearing first will begin with A, then H, then I, and at last S.

As the required word begins with A, let us take $2^{nd}$ position and find the number of words by putting remaining alphabets.

$\begin{array}{cccc}& \underset{–}{\text{Remaining letters}}& \underset{–}{\text{No. of places}}& \underset{–}{\text{No. of words}}\\ \text{A H \_ \_ \_ \_}\to & HI\underset{–}{SS}& 4& \text{= 12 words}\\ \text{A I \_ \_ \_ \_}\to & \underset{–}{\text{HH}}\underset{–}{SS}& 4& \text{= 6 words}\\ \text{A S H H \_ \_}\to & \text{I S}& 2& \text{2! = 2 words}\\ \text{A S H I H \_}\to & \text{S}& 1& \text{1! = 1 words}\end{array}$

A S H I S H comes now after all the above words.

So, number of words before ASHISH $=12+6+2+1=21$

So, rank of the word ASHISH $=22$