First slide

Permutations

Question

If all the words formed from the letters of the word HORROR are arranged in the opposite order as they are in a dictionary, then the rank of the word HORROR is

Moderate

A

56
B

87
C

58
D

59

Solution

R, R, R, O, O, H
Words starting with $R \to \frac{5!}{2! 2!} = 30$
Words starting with $O \to \frac{5!}{3!} = 20$
Words starting with $HR \to \frac{4!}{2! 2!} = 6$
The word following the above words will be "HORROR"
The next word will be "HORROR"
$∴$ Rank of the word "HORROR" = 30 + 20 + 6 + 1 + 1 = 58

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