The letters of word $O U G H T$ are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word $T O U G H$ in this dictionary.

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Solution

The correct option is D 89
Starting with G there are $4!$
Starting with H there are $4!$
Starting with O there are $4!$
Starting with TG there are $3!$
Starting with TH there are $3!$
Starting with TOG there are $2!$
Starting with TOH there are $2!$
Starting with TOUGH there are $1!$

The rank of the word TOUGH in this dictionary
$= 4! + 4! + 4! + 3! + 3! + 2! + 2! + 1! = 89^{t h} w o r d$

Hence, option 'A' is correct.

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