If the letters of the word PROUD 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 PROUD.
63
89
93
95
Given that the word is PROUD.
The lexicographic order of the letters of the given word is D, O, P, R, U. The words that begin with D will come first in the lexicographic order.
If the letter D is in the first place of the five-letter word, then the remaining four letters can be arranged in ways. On proceeding like this,
So, the rank of the word PROUD is given by,
Therefore, the rank of the word PROUD is 64
Thus, the number of words in a dictionary before the word PROUD is 64-1=63
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