Question

The letters of word $OUGHT$ are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word $TOUGH$ in this dictionary.

• A. 89
• B. 90
• C. 91
• D. 92

Answer 1

Answer: (A)

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

$=4!+4!+4!+3!+3!+2!+2!+1!={89}^{th}word$

Hence, option 'A' is correct.