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

 

Option: 1

92


Option: 2

110


Option: 3

56


Option: 4

38


Answers (1)

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Given that the word is BRAVE. 

The lexicographic order of the letters of the given word is A, B, E, R, V. 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, 

\begin{aligned} & \mathrm{A}(----)=4 ! \text { ways } \\ & \mathrm{BA}(---)=3 ! \text { ways } \\ & \mathrm{BE}(---)=3 ! \text { ways } \\ & \operatorname{BRAE}(-)\: \: =1 ! \text { ways } \\ & \mathrm{BRAVE}\: \: \: \: \: =0 \text { ! ways } \end{aligned}

So, the rank of the word BRAVE is given by

\begin{aligned} & =4 !+3 !+3 !+1 !+0 ! \\ & =(4 \times 3 \times 2 \times 1)+(3 \times 2 \times 1)+(3 \times 2 \times 1)+1+1 \\ & =24+6+6+1+1 \\ & =38 \end{aligned}

Therefore, the rank of the word BRAVE is 38

 

 

 

Posted by

Anam Khan

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