document.write( "Question 1044235: a traveling book salesperson has 5 copies of a certain statistic book, 4 copies of a certain geometry book and 3 copies of a certain calculus book. If these books are to be stored on a shelf in the sales person's van, how many distinct arrangements are possible? \n" ); document.write( "

Algebra.Com's Answer #659525 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "a traveling book salesperson has 5 copies of a certain statistic book, 4 copies of a certain geometry book
\n" ); document.write( "and 3 copies of a certain calculus book. If these books are to be stored on a shelf in the sales person's van,
\n" ); document.write( "how many distinct arrangements are possible?
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document.write( "Had all the book be distinguishable, we would have (5+4+3)! = 12! possible permutations = arrangements of the 12 books.\r\n" );
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document.write( "But for any given arrangement all other 5! arrangements that are differ by permutations of 5 copies of statistical books only, \r\n" );
document.write( "are actually considered as the same arrangement. We can not make a distinguish between such arrangements.\r\n" );
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document.write( "Therefore, we divide 12! by 5!.\r\n" );
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document.write( "Same with geometry books and the calculus book.\r\n" );
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document.write( "So, the final answer is: there are only  = 27720 arrangements.\r\n" );
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