Question

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’.

Answer 1

The words in a dictionary are arranged in alphabetical order, which for the word 'RANDOM' becomes ADMNOR.

Finding the rank of the word 'RANDOM':
(i) Starting with 'A', the remaining letters 'D', 'M', 'N', 'O', 'R' can be arranged in 5! = 120 ways. So, there are 120 words starting with 'A'.
(ii) Similarly, the number of words starting with 'M', 'N', and 'O' is also 120.
(iii) Now, the number of words starting with 'R' is also 120. Out of these words, one word is 'RANDOM'.
(iv) First, we find the words starting with 'RAD' and 'RAM'. The number of words starting with 'RAD' is 3! = 6, and the number of words starting with 'RAM' is also 3! = 6.
(v) Thus, so far, 120 + 120 + 120 + 120 + 120 + 6 + 6 = 612 words have been constructed.
(vi) Now, the words starting with 'RAN' will appear. Their number is also 3! = 6. One of these words is the word 'RANDOM' itself.
(vii) The first word beginning with 'RAN' is 'RANDMO', which is the 613th word, and the next word is 'RANDOM', making it the 614th word.

Hence, the rank of the word 'RANDOM' is 614.