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Previous Year Question (PYQs)



The 120 permutations of “MAHES” are arranged in dictionary order, as if each were an ordinary 5-letter word. The last letter of the $86^{th}$ word in the list is —





Solution

Total letters = 5 distinct → $5! = 120$ words. Fixing first letter in alphabetical order: A, E, H, M, S. Each block = $4! = 24$ words. After A (24), E (24), H (24) → total = 72. So the $86^{th}$ word lies in M-block (73–96). Within M-block, order remaining letters: A, E, H, S. Each gives $3! = 6$ words. $73$–$78$: MA… $79$–$84$: ME… $85$–$90$: MH… Hence, the $86^{th}$ word lies in MH-series. So the last letter = H.


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