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  • If the letters of the word LUCID are arranged in all possible ways and the words are arranged in a dictionary, then find the rank of the word LUCID.  <str

If the letters of the word LUCID are arranged in all possible ways and the words are arranged in a dictionary, then find the rank of the word LUCID.

 

Option: 1

92


Option: 2

89


Option: 3

93


Option: 4

95


Answers (1)

best_answer

Given that the word is LUCID. 

The lexicographic order of the letters of the given word is C, D, I, L, U. The words that begin with C will come first in the lexicographic order.

If the letter C 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{C}(----)=4 ! \text { ways } \\ & \mathrm{D}(----)=4 ! \text { ways } \\ & \mathrm{I}(----)=4 ! \text { ways } \\ & \mathrm{LC}(---)=3 ! \text { ways } \\ & \mathrm{LD}(---)=3 ! \text { ways } \\ & \mathrm{LI}(---)=3 ! \text { ways } \\ & \mathrm{LUCD}(-)=1 ! \text { ways } \\ & \mathrm{LUCID}=0 \text { ! ways } \end{aligned}

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

\begin{aligned} & =4 !+4 !+4 !+3 !+3 !+3 !+1 !+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)+(3 \times 2 \times 1)+1+1 \\ & =24+24+24+6+6+6+1+1 \\ & =92 \end{aligned}

Therefore, the rank of the word LUCID is 92

Posted by

jitender.kumar

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