Question

The letters of the word "DANGER" are permuted in all possible ways and the words thus formed are arranged as in a dictionary. The rank of the word "DANGER" is
A) 132
B) 133
C) 134
D) 135

Answer 1

Hint: In this type of question we need to check if any letter is being repeated or not. But there is no repetition, If there are n different things then the total number of arrangements possible is = n!
We will use the above concept.

Complete step by step answer:
The letters of the word "DANGER" are permuted in all possible ways and the words thus formed are arranged as in a dictionary, i.e in the alphabetical order.
Total number of letters in the word “DANGER” are 6.

We will arrange every letter according to sequence in the dictionary.
A _ _ _ _ _
Fix A at first place then arranging the remaining 5 letters =5!
Number of words starting with A =5!.

After A, D will be there at first place but in our word, D is also at first place so we will owe the letter at second place.
DA _ _ _ _
In the given word A is also at second place so we will move to the letter at third place.

DAE _ _ _
Number of words starting with DAE can be written in 3! ways.
After E, G will be there at third place.
Number of words starting with DAG =3!

Next following words are DANEGR, DANERG and DANGER
∴ Rank of the word 'DANGER' = 5! + 3! + 3! + 1 + 1 + 1
 = 120 + 6 + 6 + 3
 = 135
Hence, option (D) is correct.

Note: In this type of question we need to move forward letter by letter by keeping all the letters in mind in alphabetical order, and the most important we should take care of repetition of letters also.