document.write( "Question 1034761: How many ways 10 hats of different colours can be put on the heads of 10 boys sitting in a row,so that the red and black coloured hats can never be put on the heads of any two adjacent boys ? \n" ); document.write( "
Algebra.Com's Answer #652814 by Edwin McCravy(20055)\"\" \"About 
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How many ways 10 hats of different colours can be put on
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document.write( "The answer would be 10! if there were no restrictions.\r\n" );
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document.write( "If the hats were:\r\n" );
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document.write( "A B C D E F G H I J\r\n" );
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document.write( "and there were no restrictions they could be arranged in 10! ways\r\n" );
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document.write( "From that 10! we must subtract the number of non-allowable ways.\r\n" );
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document.write( "Suppose the red hat is hat A and the black hat is hat B.\r\n" );
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document.write( "Then we must subtract the 9! ways they could be\r\n" );
document.write( "arranged with hat A and hat B together, with hat A \r\n" );
document.write( "left of B:\r\n" );
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document.write( "AB C D E F G H I J\r\n" );
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document.write( "And we must also subtract the 9! ways they could be\r\n" );
document.write( "arranged with hat A and hat B together, with hat B left \r\n" );
document.write( "of hat A:\r\n" );
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document.write( "BA C D E F G H I J\r\n" );
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document.write( "Answer: 10! - 2*9! = 3628800 - 2*(362880) = 2903040\r\n" );
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document.write( "Edwin
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