document.write( "Question 514613: How many ways can the digits 1, 2, 3, 4, and 5 be arranged in a row of 3 to form an odd counting number if repetition is permitted and if 3 cannot be second and 1 cannot be third? \n" ); document.write( "
Algebra.Com's Answer #343500 by Edwin McCravy(20056)\"\" \"About 
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How many ways can the digits 1, 2, 3, 4, and 5 be arranged in a row of 3 to form an odd counting number if repetition is permitted and if 3 cannot be second and 1 cannot be third?\r
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document.write( "There are no restrictions on the first digit, so we can\r\n" );
document.write( "choose it any of 5 ways.\r\n" );
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document.write( "For each of the 5 ways to choose the first digit there are\r\n" );
document.write( "4 ways to choose the 2nd digit, either 1,2,4, or 5. We are\r\n" );
document.write( "told it can't be 3. That's 5*4 or 20 ways to choose the first \r\n" );
document.write( "two digits.\r\n" );
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document.write( "An odd number must end in an odd digit, so the third digit is \r\n" );
document.write( "either 1,3, or 5. But we are told 1 cannot be third, so it can \r\n" );
document.write( "only be 3 or 5. So for each of the 20 ways to choose the first \r\n" );
document.write( "and second digits, there are 2 ways to choose the last digit.\r\n" );
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document.write( "That makes 20*2 or 40 ways total.\r\n" );
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document.write( "Here they all are:\r\n" );
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document.write( "1.  113\r\n" );
document.write( "2.  115\r\n" );
document.write( "3.  123\r\n" );
document.write( "4.  125\r\n" );
document.write( "5.  143\r\n" );
document.write( "6.  145\r\n" );
document.write( "7.  153\r\n" );
document.write( "8.  155\r\n" );
document.write( "9.  213\r\n" );
document.write( "10.  215\r\n" );
document.write( "11.  223\r\n" );
document.write( "12.  225\r\n" );
document.write( "13.  243\r\n" );
document.write( "14.  245\r\n" );
document.write( "15.  253\r\n" );
document.write( "16.  255\r\n" );
document.write( "17.  313\r\n" );
document.write( "18.  315\r\n" );
document.write( "19.  323\r\n" );
document.write( "20.  325\r\n" );
document.write( "21.  343\r\n" );
document.write( "22.  345\r\n" );
document.write( "23.  353\r\n" );
document.write( "24.  355\r\n" );
document.write( "25.  413\r\n" );
document.write( "26.  415\r\n" );
document.write( "27.  423\r\n" );
document.write( "28.  425\r\n" );
document.write( "29.  443\r\n" );
document.write( "30.  445\r\n" );
document.write( "31.  453\r\n" );
document.write( "32.  455\r\n" );
document.write( "33.  513\r\n" );
document.write( "34.  515\r\n" );
document.write( "35.  523\r\n" );
document.write( "36.  525\r\n" );
document.write( "37.  543\r\n" );
document.write( "38.  545\r\n" );
document.write( "39.  553\r\n" );
document.write( "40.  555\r\n" );
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document.write( "Edwin
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