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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’. |
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Answer» The words in a dictionary are written in an alphabetical order, which, here is ADMNOR. (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, number of words starting with M = 120, starting with N = 120, and starting with O =120. (iii) Now, the number of words starting with R is also 120. Out of these words, one word is RANDOM. First, we find the words starting with RAD and RAM. Number of starting with RAD = 3! = 6 Number of starting with RAM = 3! = 6 (iv) Thus, so far, 120 + 120 + 120 + 120 + 120 + 6 + 6 = 612 words have been constructed. (v) Now, the words starting with RAN will appear. Their number is also = 3! = 6. One of these words is the word RANDOM itself. The first word beginning with RAN is RANDMO. It is 613th word and so the next word is RANDOM. RANDOM is the 614th word. Hence, rank of RANDOM = 614. |
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