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| 1. |
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 |
| Answer» <p style="text-align:justify"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000"><strong>Correct option (1) 169194</strong></span></span></p><p style="text-align:justify"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000"><strong>Explanation:</strong></span></span></p><p style="text-align:justify"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">(a) Total number of permutations</span></span></p><p style="text-align:justify"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">= 9!/2 ,since N is repeated.</span></span></p><p style="text-align:justify"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">(b) Number of permutations in which 'HIN' comes as a block = 7!</span></span></p><p style="text-align:justify"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">Number of permutations in which 'TAN' comes as a block = 7! Number of permutations in which</span></span></p><p style="text-align:justify"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">'DUS' comes as a block = 7!/2</span></span></p><p style="text-align:justify"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">(c) This includes both 'HIN' and 'TAN' comes as blocks = 5! same is true for the other two pairs. </span></span></p><p style="text-align:justify"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">(d) Number of permutations in which all three blocks come = 3! </span></span></p><p style="text-align:justify"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">∴ required number of permutations</span></span></p><p style="text-align:justify"></p> | |