document.write( "Question 466320: an elevator in a building starts with 6 people and stops at 8 floors.suppose ,all permutations of the passengers getting off at various floors are equally likely,find the probability that at least 2 of them get off on the same floor. \n" ); document.write( "

Algebra.Com's Answer #319671 by Edwin McCravy(20056) $\"\"$ $\"About$

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an elevator in a building starts with 6 people and stops at 8 floors.suppose ,all permutations of the passengers getting off at various floors are equally likely,find the probability that at least 2 of them get off on the same floor.
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document.write( "We will get the probability of the complement event, where no more\r\n" );
document.write( "than 1 person gets off at any floor, and then subtract that from 1:\r\n" );
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document.write( "Each of the 6 people has in mind one of those 8 floors as his or her \r\n" );
document.write( "exit floor.\r\n" );
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document.write( "We will get the denominator of the probability first:\r\n" );
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document.write( "Suppose the 6 people line up in a single file to enter the elevator.\r\n" );
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document.write( "Then \r\n" );
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document.write( "We can choose the exit floor for the 1st person any of 8 ways\r\n" );
document.write( "We can choose the exit floor for the 2nd person any of 8 ways\r\n" );
document.write( "We can choose the exit floor for the 3rd person any of 8 ways\r\n" );
document.write( "We can choose the exit floor for the 4th person any of 8 ways\r\n" );
document.write( "We can choose the exit floor for the 5th person any of 8 ways\r\n" );
document.write( "We can choose the exit floor for the 6th person any of 8 ways\r\n" );
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document.write( "That's 8⁶ ways to choose their exit floors.  That is the denominator\r\n" );
document.write( "of the probability, the total number of choices of exit floors\r\n" );
document.write( "for all 6 people.\r\n" );
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document.write( "The numerator of the complement event is the number of ways\r\n" );
document.write( "each has a different exit floor.  \r\n" );
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document.write( "We can choose the exit floor for the 1st person any of 8 ways\r\n" );
document.write( "We can choose the exit floor for the 2nd person any of 7 ways\r\n" );
document.write( "We can choose the exit floor for the 3rd person any of 6 ways\r\n" );
document.write( "We can choose the exit floor for the 4th person any of 5 ways\r\n" );
document.write( "We can choose the exit floor for the 5th person any of 4 ways\r\n" );
document.write( "We can choose the exit floor for the 6th person any of 3 ways\r\n" );
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document.write( "That's 8·7·6·5·4·3 or 8P6 ways to choose their exit floors for\r\n" );
document.write( "the complement event.  That is the numerator of the probability \r\n" );
document.write( "of the complement event.  So the probability of the complement\r\n" );
document.write( "event is\r\n" );
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document.write( "= .0769042969\r\n" );
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document.write( "So the desired probability is 1 - .0769042969 = .9230957031\r\n" );
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document.write( "or in exact form \r\n" );
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document.write( "Edwin

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