If all the letters of the word ‘RAPID’ are arranged in all possible manner as they are in a dictionary, then find the rank of the word ‘RAPID’.

Solution :

First of all, arrange all letters of given word alphabetically : ‘ADIPR’

Total number of words starting with A _ _ _ _ = 4! = 24

Total number of words starting with D _ _ _ _ = 4! = 24

Total number of words starting with I _ _ _ _ = 4! = 24

Total number of words starting with P _ _ _ _ = 4! = 24

Total number of words starting with R A D _ _ = 2! = 2

Total number of words starting with R A I _ _ = 2! = 2

Total number of words starting with R A P D _ = 1 = 1

Total number of words starting with R A P I _ = 1 = 1

Therefore, Rank of the word RAPID = 24 + 24 + 24 + 24 + 2 + 2 + 1 + 1 = 102

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