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If the letters of the word LIGHT 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 LIGHT.

 

Option: 1

63


Option: 2

89


Option: 3

84


Option: 4

95


Answers (1)

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Given that the word is LIGHT. 

The lexicographic order of the letters of the given word is G, H, I, L, T. The words that begin with G will come first in the lexicographic order.

If the letter G 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, 

\begin{aligned} & \mathrm{G}(----)=4 ! \text { ways } \\ & \mathrm{H}(----)=4 ! \text { ways } \\ & \mathrm{I}(----)=4 ! \text { ways } \\ & \mathrm{LG}(---)=3 ! \text { ways } \\ & \mathrm{GH}(---)=3 ! \text { ways } \\ & \mathrm{LIGHT}=0 \text { ! ways } \end{aligned}

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

\begin{aligned} & =4 !+4 !+4 !+3 !+3 !+0 ! \\ & =(4 \times 3 \times 2 \times 1)+(4 \times 3 \times 2 \times 1)+(4 \times 3 \times 2 \times 1)+(3 \times 2 \times 1)+(3 \times 2 \times 1)+1 \\ & =24+24+24+6+6+1 \\ & =85 \end{aligned}

Therefore, the rank of the word LIGHT is 85

Thus, the number of words in a dictionary before the word LIGHT is 85-1=84

 

Posted by

Shailly goel

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