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

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

 

Option: 1

625


Option: 2

1316


Option: 3

13


Option: 4

772


Answers (1)

best_answer

Given that the word is HAPPY.

The lexicographic order of the letters of the given word is A, H, P, P, Y. 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(----)=\frac{4 !}{2 !} \text { ways }

Happy=0!\; ways

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

\begin{aligned} & =\frac{4 !}{2 !}+0 ! \\ & =(4 \times 3)+1 \\ & =13 \end{aligned}

Therefore, the rank of the word HAPPY is 13

Posted by

shivangi.shekhar

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