Question

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

• A. $530$
• B. $480$
• C. $531$
• D. $481$

Answer 1

The correct option is A $530$

In the alphabetic order the letters are $C,C,E,I,K,R,T$. Words beginning with $C$ will be printed at first. Our word also begins with $C$.

The no. of words beginning with $C$ and having $C$ or $E$ and $I$ or $R$ in second place $=4\times 5!$

The no. of words begin with $CR$ and having $C$ or $E$ in the third place$=2\times 4!$

The no. of words begin with $CRIC$ and having $E$ in the fifth place$=2!$

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

$\therefore$ The required place for the word $CRICKET$ is $=(4\times 5!+2\times 4!+2!)+1=530$

$\therefore$ The word will be printed in ${530}^{th}$ place.