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  • If the letters of the word DEAR 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 DEAR.  <

If the letters of the word DEAR 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 DEAR.

 

Option: 1

63


Option: 2

8


Option: 3

84


Option: 4

80


Answers (1)

best_answer

Given that the word is DEAR. 

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

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

\begin{aligned} & \mathrm{A}(---)=3 ! \text { ways } \\ & \mathrm{DA}(--)=2 ! \text { ways } \\ & \mathrm{DEAR}=0 \text { ! ways } \end{aligned}

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

\begin{aligned} & =3 !+2 !+0 ! \\ & =(3 \times 2 \times 1)+(2 \times 1)+1 \\ & =6+2+1 \\ & =9 \end{aligned}

Therefore, the rank of the word DEAR is 8

Thus, the number of words in a dictionary before the word DEAR is 9-1=8

Posted by

avinash.dongre

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