document.write( "Question 1204981: If n is an integer between 1 and 96 (inclusive), what is the probability that n(n+1)(n+2) is divisible by 8?
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Algebra.Com's Answer #841554 by ikleyn(52858) $\"\"$ $\"About$

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\n" ); document.write( "If n is an integer between 1 and 96 (inclusive), what is the probability that n(n+1)(n+2) is divisible by 8?
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document.write( "Consider the REDUCED set of numbers  {1,2,3,4,5,6,7,8}.\r\n" );
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document.write( "Count, how many times n*(n+1)*(n+2) is divisible by 8 for n = 1,2,3,4,5,6,7,8\r\n" );
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document.write( "   T     A     B     L     E\r\n" );
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document.write( "n    n*(n+1)*(n+2)   divisibility\r\n" );
document.write( "                        by 8\r\n" );
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document.write( "1         6\r\n" );
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document.write( "2        24             (*) \r\n" );
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document.write( "3        60    \r\n" );
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document.write( "4       120             (*)\r\n" );
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document.write( "5       210\r\n" );
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document.write( "6       336             (*)\r\n" );
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document.write( "7       504             (*)\r\n" );
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document.write( "8       720             (*)\r\n" );
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document.write( "In the table, I marked all these cases (*) and got 5 cases of divisibility by 8.\r\n" );
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document.write( "This picture will repeat cyclically every 8 consecutive positive integer numbers.\r\n" );
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document.write( "So, the probability under the problem's question is  5/8.    ANSWER\r\n" );
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