Question

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

• A. $89$
• B. $90$
• C. $91$
• D. $92$

Answer 1

The correct option is A $89$

Letters present in the word $OUGHT$ are $O,U,G,H,T.$
Order of the letters according to the alphabet is $G,H,O,T,U.$
Number of words starting with $G$ $\left(G\_\_\_\_\right)$ is $4!$.
Number of words starting with $H$ $\left(H\_\_\_\_\right)$ is $4!$.
Number of words starting with $O$ $\left(O\_\_\_\_\right)$ is $4!$.
Number of words starting with $TG$ $\left(TG\_\_\_\right)$ is $3!$.
Number of words starting with $TH$ $\left(TH\_\_\_\right)$ is $3!$.
Number of words starting with $TOG$ $\left(TOG\_\_\right)$ is $2!$.
Number of words starting with $TOH$ $\left(TOH\_\_\right)$ is $2!$.
Then the next word will be $TOUGH$.

$\therefore$ The rank of the word $TOUGH$
$=4!+4!+4!+3!+3!+2!+2!+1=89$