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

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

 

Option: 1

92


Option: 2

89


Option: 3

93


Option: 4

95


Answers (1)

best_answer

Given that the word is QUICK. 

The lexicographic order of the letters of the given word is C, I, K, Q, 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,

$$ C(----)=4 ! $$\; way

\begin{aligned} & \mathrm{I}(----)=4 ! \text { ways } \\ & \mathrm{K}(----)=4 ! \text { ways } \\ & \mathrm{QC}(---)=3 ! \text { ways } \\ & \mathrm{Ql}(---)=3 ! \text { ways } \\ & \mathrm{QK}(---)=3 ! \text { ways } \end{aligned}

\operatorname{QUC}(--)=2 !\; ways

\text { QUICK }=0 \text { ! ways }

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


\begin{aligned} & =4 !+4 !+4 !+3 !+3 !+3 !+2 !+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)+(2 \times 1)+1 \\ & =24+24+24+6+6+6+2+1 \\ & =93 \end{aligned}

Posted by

seema garhwal

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