# The letters of the word 'RANDOM' are written in all possible ways and these words are written out as in a dictionary.Find the rank of the word 'RANDOM'?

602thword is random

• -62

Hi!

The given word is RANDOM. In a dictionary the words are arranged in alphabetical order. The words beginning with A, D, M, N, O and R are written in order.
Number of words starting with A = 5! = 120
Number of words starting with D = 5! = 120
Number of words starting with M = 5! = 120
Number of words starting with N = 5! = 120
Number of words starting with O = 5! = 120

Number of words beginning with R = 5! = 120, but one of these words is word RANDOM.
Firstly consider the words starting with RAD and RAM.
Number of words beginning with RAD = 3! = 6
Number of words beginning with RAM = 3! = 6
There are 3! words beginning with RAN one of these words is the word RANDOM itself.
The first word beginning with RAN is the word RANDMO and the next word is RANDOM.
∴ Rank of RANDOM = 5 × 120 + 2 × 6 + 2 = 614

Cheers!

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