Question

In all the words formed from the letters of the word HORROR are arranged in the opposite order as they are in dictionary, then the rank of the word HORROR is:
A. 56
B. 57
C. 58
D. 59

Answer 1

Hint: We will first mention the preferences’ opposite in the dictionary. Then, we will find the word closest to the word we require and then move step by step to it.

Complete answer:
We can see that the word HORROR consists of 3 different letters H, O and R.
Among these H comes in first place in the dictionary, then comes O and the last word is R.
So, if we reverse the directions of everything, we get the first one as R, then O and the last one as H.
Now, if we look at the word made by R, HORROR definitely stands way later than this.
So, let us first calculate how many words we form with R.
$ \Rightarrow $Words formed with R = $\dfrac{{5!}}{{2! \times 2!}}$
Now, we know that n! = n.(n-1).(n-2)……….1
So, we have:-
$ \Rightarrow $Words formed with R = $\dfrac{{5 \times 4 \times 3 \times 2}}{{2 \times 2}}$
Simplifying it, we will get:-
$ \Rightarrow $Words formed with R = $5 \times 3 \times 2$
Simplifying the calculations further, we will then obtain:-
$ \Rightarrow $Words formed with R = 30
Now, after these 30 words, we get the words starting from O:
HORROR still stands after these words end.
$ \Rightarrow $Words formed with O = $\dfrac{{5!}}{{3!}}$
Now, we know that n! = n.(n-1).(n-2)……….1
So, we have:-
$ \Rightarrow $Words formed with O = $\dfrac{{5 \times 4 \times 3 \times 2}}{{3 \times 2}}$
Simplifying it, we will get:-
$ \Rightarrow $Words formed with O = $5 \times 4$
Simplifying the calculations further, we will then obtain:-
$ \Rightarrow $Words formed with O = 20
Now, we start forming words with H and we need to get HORROR, so we cannot calculate all the words we form with ‘H’.
Now, we know that O comes after R in this dictionary because we have reversed the preferences. So, we will calculate the words we form with HR now:-
$ \Rightarrow $Words formed with HR = $\dfrac{{4!}}{{2! \times 2!}}$
Now, we know that n! = n.(n-1).(n-2)……….1
So, we have:-
$ \Rightarrow $Words formed with HR = $\dfrac{{4 \times 3 \times 2}}{{2 \times 2}}$
Simplifying it, we will get:-
$ \Rightarrow $Words formed with HR = $3 \times 2$
Simplifying the calculations further, we will then obtain:-
$ \Rightarrow $Words formed with HR = 6
Now, we have completed 30 + 20 + 6 = 56 words.
Now, we come to start making words with HO:-
Now, if we fix HO we have 4 spaces to fill. We are left with the alphabets 3 R’s and 1 O.
Now, since in this dictionary we have the first preference of R.
So, the first word we get with HO is HORRRO.
Now, the second word will be HORROR.
Therefore, we have crossed 56 + 1 = 57 words to reach this.
This is the fifty eighth word.

$\therefore $ the correct option is (C).

Note:
The students must note that while calculating the number of words we have some factorial terms in the denominator. That is because of repetition of alphabets. We have R repeating thrice and we are keeping the first alphabet fixed, therefore, we are moving the other letters and taking 5! In the numerator and so on.