Question

The letters of the word CRICKET are permuted in all possible ways and the words thus formed are rearranged as in a dictionary. The rank of the word CRICKET is
A. 243
B. 452
C. 531
D. 729

Answer 1

Hint: In order to get the right answer we need to order the letters in the word CRICKET in alphabetical order then follow the rules to find a word in the dictionary. That is we have to follow the sequence to get the required word. Doing this will solve your problem and will give you the right answer.

Complete step-by-step answer:
We know that the alphabetical order of the letters of the given word CRICKET is C,C,E,I,K,R,T

$ \Rightarrow $The number of words beginning with CC will be 5! This is because CC will be one letter and is fixed at first and second place. We can arrange now 5 letters so the arrangement of 5 letters is 5! = 120.


$ \Rightarrow $The number of words beginning with CE will be 5! This is because CE will be one letter and is fixed at first and second place. We can arrange now 5 letters so the arrangement of 5 letters is 5! = 120.


$ \Rightarrow $The number of words beginning with CI will be 5! This is because CI will be one letter and is fixed at first and second place. We can arrange now 5 letters so the arrangement of 5 letters is 5! = 120.

$ \Rightarrow $The number of words beginning with CK will be 5! This is because CK will be one letter and is fixed at first and second place. We can arrange now 5 letters so the arrangement of 5 letters is 5! = 120.

$ \Rightarrow $The number of words beginning with CRC will be 4! This is because CRC will be one letter and is fixed at first, second and third place. We can arrange now 4 letters so the arrangement of 4 letters is 4! = 24.

$ \Rightarrow $The number of words beginning with CRE will be 4! This is because CRE will be one letter and is fixed at first, second and third place. We can arrange now 4 letters so the arrangement of 4 letters is 4! = 24.

$ \Rightarrow $The number of words beginning with CRICE will be 2! This is because CRICE will be one letter and is fixed at first, second, third, fourth and fifth place. We can arrange now 2 letters so the arrangement of 2 letters is
2!= 2.
Then we can say that the next word is CRICKET
Rank is 120+120+120+120+24+24+2+1=531
 So, the correct option is C.

Note: To find a word in a dictionary you have to go to the words alphabet from which the word is started then you need to look at the second letter of the word, and then the third, and so on, in order to find it. It takes a little practice to find words quickly. You may need to scan several pages of the dictionary in order to find the word that you need. Here we used the number of arrangements the words can have then we have found the rank by adding 1 to the total number of words we got from the arrangement of all the possible words.