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  • If the letters of the word GREAT 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 GREAT. &nbsp

If the letters of the word GREAT 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 GREAT.

 

Option: 1

63


Option: 2

62


Option: 3

93


Option: 4

95


Answers (1)

best_answer

Given that the word is GREAT. 

The lexicographic order of the letters of the given word is A, E, G, 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 4! ways. On proceeding like this, 

$$ A(----)=4 \text { ! }\: $$ ways

E(----)=4 !\; $$ ways

\mathrm{GA}(---)=3 ! ways\\ \mathrm{GE}(---)=3 ! ways\\ \operatorname{GRA}(--)=2 ! ways\\ GREAT =0 ! ways

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

\begin{aligned} & =4 !+4 !+3 !+3 !+2 !+0 ! \\ & =(4 \times 3 \times 2 \times 1)+(4 \times 3 \times 2 \times 1)+(3 \times 2 \times 1)+(3 \times 2 \times 1)+(2 \times 1)+1+1 \\ & =24+24+6+6+2+1 \\ & =63 \end{aligned}

Therefore, the rank of the word GREAT is  63

Thus, the number of words in a dictionary before the word GREAT is 63-1=62
 

 

Posted by

SANGALDEEP SINGH

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