## 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