Question

A dictionary is printed consisting of $7$ lettered words only that can be made with a letter of the word $CRICKET$. If the words are printed in alphabetical order, as in an ordinary dictionary, then the number of words before the word $CRICKET$ is?

• A. 530
• B. 480
• C. 531
• D. 481

Answer 1

The correct option is A

530

Step1. Calculate the number of words for each possibility :

Given: a dictionary is made from letter $CRICKET$

First, we have to arrange all the alphabet of the word $CRICKET$ in alphabetical order.

$\mathrm{C},\mathrm{C},\hspace{0.17em}\mathrm{E},\hspace{0.17em}\mathrm{I},\mathrm{K},\hspace{0.17em}\mathrm{R},\mathrm{T}$

The first Printed word begins with the alphabet $C$.

Word cricket also starts with the alphabet$C$.

The number of words beginning with $C$ and second place filled with $C$ or $E$ and $I$ or $R$ $=4\times 5!$

The number of words begins with $CR$ as a fixed position and having $C$ or $E$ in the third position$=2\times 4!$

The number of words begins with $CRIC$ and having $E$ in the fifth position$=2!$

Step2. Calculate the position of the word CRICKET:

After printing all the above three words, the word $CRICKET$ will be printed.

Therefore, the required position for the word $CRICKET$is$=\left[\left(4\times 5!\right)+\left(2\times 4!\right)+2!\right]+1$

Therefore, the number of words printed before the word cricket is $=530$

Hence, Option ( A) is the correct answer.