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The number of permutations of the word HINDUSTAN such that none of the three patterns HIN, DUS, TAN occurs is (1) 169194 (2) 166680 (3) 169190 (4) 166670 |
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Answer» Correct option (1) 169194 Explanation: (a) Total number of permutations = 9!/2 ,since N is repeated. (b) Number of permutations in which 'HIN' comes as a block = 7! Number of permutations in which 'TAN' comes as a block = 7! Number of permutations in which 'DUS' comes as a block = 7!/2 (c) This includes both 'HIN' and 'TAN' comes as blocks = 5! same is true for the other two pairs. (d) Number of permutations in which all three blocks come = 3! ∴ required number of permutations |
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