document.write( "Question 1182760: In how many ways can the numbers 1,2,3,4,5,6 be arranged in a row so that the product of any 2 adjacent numbers is even? \n" ); document.write( "

Algebra.Com's Answer #812839 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "These arrangements are those and only those, where for each odd number its closest neighbors are even numbers.\r\n" );
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document.write( "In other words, these arrangements are those, where odd and even numbers occupy alternate positions.\r\n" );
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document.write( "There are 3! = 6 arrangements for the three ODD numbers in such permutations, and 3! = 6  arrangements \r\n" );
document.write( "for the three EVEN numbers in such permutations.\r\n" );
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document.write( "Do not forget to include factor 2 to account to which number, - an odd or an even, - goes first.\r\n" );
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document.write( "So, the ANSWER  is:  there are  2*6*6 = 72  such arrangements.\r\n" );
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