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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

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B

480

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C

531

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D

481

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Solution

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.

C,C,E,I,K,R,T

The first Printed word begins with the alphabet C.

Word cricket also starts with the alphabetC.

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

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

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 CRICKETis=4×5!+2×4!+2!+1

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

Hence, Option ( A) is the correct answer.


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