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  • If the letters of the word ALERT are arranged in all possible ways and the words are arranged in a dictionary, then find the number of words in the dictionary before the word ALERT. &nbsp

If the letters of the word ALERT are arranged in all possible ways and the words are arranged in a dictionary, then find the number of words in the dictionary before the word ALERT.

 

Option: 1

63


Option: 2

8


Option: 3

84


Option: 4

6


Answers (1)

best_answer

Given that the word is ALERT. 

The lexicographic order of the letters of the given word is A, E, L, R, T. The words that begin with A will come first in the lexicographic order.

If the letter A is in the first place of the five-letter word, then the remaining four letters can be arranged in 3! ways. On proceeding like this, 

\mathrm{AE}(---)=3\: !

\mathrm{ALERT}=0 ! \; ways

So, the rank of the word ALERT is given by,

\begin{aligned} & =3 !+0 ! \\ & =(3 \times 2 \times 1)+1 \\ & =6+1 \\ & =7 \end{aligned}

Therefore, the rank of the word ALERT is 7.

Thus, the number of words in a dictionary before the word ALERT is 7-1=6

Posted by

Irshad Anwar

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