document.write( "Question 83529: A three-digit number is formed by selecting from the digits 1,2,3,4,5 and 6 with no repitition. How many of these three digit numbers will have a number greater than 300? \n" ); document.write( "
Algebra.Com's Answer #60058 by Edwin McCravy(20055) $\"\"$ $\"About$
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document.write( "A three-digit number is formed by selecting from the digits 1,2,3,4,5 and 6\r\n" );
document.write( "with no repitition. How many of these three digit numbers will have a number\r\n" );
document.write( "greater than 300?\r\n" );
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document.write( "Take a typical sample three-digit number, say:\r\n" );
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document.write( "                 523\r\n" );
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document.write( "We can choose the digit where the \"5\" is in 4 different ways, as 3,4,5, or 6.\r\n" );
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document.write( "Having chosen the first digit any of those 4 ways, that leaves 5 of the 6 that\r\n" );
document.write( "weren't chosen as the first digit that can be chosen for the second digit,\r\n" );
document.write( "where the \"2\" is in the sample.  So there are 4×5 or 20 ways to choose the\r\n" );
document.write( "first two digits, to go where the \"52\" is.\r\n" );
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document.write( "Having chosen the first two digits any of those 4×5 or 20 ways, that leaves 4\r\n" );
document.write( "of the original 6 that weren't chosen as either the first digit or the second\r\n" );
document.write( "digit that can be chosen for the third digit, where the \"3\" is in the sample.\r\n" );
document.write( "So there are 4×5×4 or 80 ways to choose the three digits. \r\n" );
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document.write( "Here are the 80 ways listed:\r\n" );
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document.write( "1.  312\r\n" );
document.write( "2.  314\r\n" );
document.write( "3.  315\r\n" );
document.write( "4.  316\r\n" );
document.write( "5.  321\r\n" );
document.write( "6.  324\r\n" );
document.write( "7.  325\r\n" );
document.write( "8.  326\r\n" );
document.write( "9.  341\r\n" );
document.write( "10.  342\r\n" );
document.write( "11.  345\r\n" );
document.write( "12.  346\r\n" );
document.write( "13.  351\r\n" );
document.write( "14.  352\r\n" );
document.write( "15.  354\r\n" );
document.write( "16.  356\r\n" );
document.write( "17.  361\r\n" );
document.write( "18.  362\r\n" );
document.write( "19.  364\r\n" );
document.write( "20.  365\r\n" );
document.write( "21.  412\r\n" );
document.write( "22.  413\r\n" );
document.write( "23.  415\r\n" );
document.write( "24.  416\r\n" );
document.write( "25.  421\r\n" );
document.write( "26.  423\r\n" );
document.write( "27.  425\r\n" );
document.write( "28.  426\r\n" );
document.write( "29.  431\r\n" );
document.write( "30.  432\r\n" );
document.write( "31.  435\r\n" );
document.write( "32.  436\r\n" );
document.write( "33.  451\r\n" );
document.write( "34.  452\r\n" );
document.write( "35.  453\r\n" );
document.write( "36.  456\r\n" );
document.write( "37.  461\r\n" );
document.write( "38.  462\r\n" );
document.write( "39.  463\r\n" );
document.write( "40.  465\r\n" );
document.write( "41.  512\r\n" );
document.write( "42.  513\r\n" );
document.write( "43.  514\r\n" );
document.write( "44.  516\r\n" );
document.write( "45.  521\r\n" );
document.write( "46.  523\r\n" );
document.write( "47.  524\r\n" );
document.write( "48.  526\r\n" );
document.write( "49.  531\r\n" );
document.write( "50.  532\r\n" );
document.write( "51.  534\r\n" );
document.write( "52.  536\r\n" );
document.write( "53.  541\r\n" );
document.write( "54.  542\r\n" );
document.write( "55.  543\r\n" );
document.write( "56.  546\r\n" );
document.write( "57.  561\r\n" );
document.write( "58.  562\r\n" );
document.write( "59.  563\r\n" );
document.write( "60.  564\r\n" );
document.write( "61.  612\r\n" );
document.write( "62.  613\r\n" );
document.write( "63.  614\r\n" );
document.write( "64.  615\r\n" );
document.write( "65.  621\r\n" );
document.write( "66.  623\r\n" );
document.write( "67.  624\r\n" );
document.write( "68.  625\r\n" );
document.write( "69.  631\r\n" );
document.write( "70.  632\r\n" );
document.write( "71.  634\r\n" );
document.write( "72.  635\r\n" );
document.write( "73.  641\r\n" );
document.write( "74.  642\r\n" );
document.write( "75.  643\r\n" );
document.write( "76.  645\r\n" );
document.write( "77.  651\r\n" );
document.write( "78.  652\r\n" );
document.write( "79.  653\r\n" );
document.write( "80.  654\r\n" );
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document.write( "Edwin
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