document.write( "Question 980989: 1. Four trumpet players' instruments are mixed up, and the trumpets are given to the players just before a concert. What is the probability that no one gets his or her trumpet back? \n" ); document.write( "

Algebra.Com's Answer #602054 by Edwin McCravy(20065) $\"\"$ $\"About$

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document.write( "Given n things in a certain order, the number of \"derangements\" or \r\n" );
document.write( "ways to rearrange them so that none of them are in the same position\r\n" );
document.write( "they were in before rearranging is given by the formula !n, known as \r\n" );
document.write( "n-subfactorial.\r\n" );
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document.write( "The formula for !n is \r\n" );
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document.write( "So the number of ways no trumpet player gets his or her own trumpet back is\r\n" );
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document.write( "[Incidentally, FYI, those 9 rearrangements of \r\n" );
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document.write( "1,2,3,4 are\r\n" );
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document.write( "2,1,4,3\r\n" );
document.write( "2,3,4,1\r\n" );
document.write( "2,4,1,3\r\n" );
document.write( "3,1,4,2\r\n" );
document.write( "3,4,1,2\r\n" );
document.write( "3,4,2,1\r\n" );
document.write( "4,1,2,3\r\n" );
document.write( "4,3,1,2\r\n" );
document.write( "4,3,2,1]\r\n" );
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document.write( "The total number of arrangements is 4! = 24.\r\n" );
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document.write( "So the desired probability is 9 ways out of 24.\r\n" );
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document.write( "That's 9/24\r\n" );
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document.write( "Edwin

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