document.write( "Question 1200908: Suppose you have 30 books (15 novels, 10 history books, and 5 math books). Assume that all 30 books are different.
\n" ); document.write( "In how many ways can you put the 30 books in a row on a shelf?
\n" ); document.write( "In how many ways can you get a bunch of four books to give to a friend?
\n" ); document.write( "In how many ways can you get a bunch of three history books and seven novels to give to a friend?
\n" ); document.write( "In how many ways can you put the 30 books in a row on a shelf if the novels are on the left, the math books are in the middle, and the history books are on the right?
\n" ); document.write( "In how many ways can you put the 30 books in a row on a shelf if the five math books are to be grouped together, but there are no restrictions on the placement of the other books? \n" ); document.write( "

Algebra.Com's Answer #835289 by math_helper(2461) $\"\"$ $\"About$

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document.write( "Suppose you have 30 books (15 novels, 10 history books, and 5 math books). Assume that all 30 books are different.
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document.write( "In how many ways can you put the 30 books in a row on a shelf? 
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document.write( "   30!   (where n! = n*(n-1)*(n-2)*...*3*2*1)\r
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document.write( "In how many ways can you get a bunch of four books to give to a friend?
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document.write( "   C(30,4)  where  C(n,r) = n!/((n-r)!r!)\r
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document.write( "In how many ways can you get a bunch of three history books and seven novels to give to a friend?
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document.write( "   C(10,3)*C(15,7)\r
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document.write( "In how many ways can you put the 30 books in a row on a shelf if the novels are on the left, the math books are in the middle, and the history books are on the right?
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document.write( "    15!*5!*10!\r
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document.write( "In how many ways can you put the 30 books in a row on a shelf if the five math books are to be grouped together, but there are no restrictions on the placement of the other books? 
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document.write( "  
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document.write( "    Treat the 5 math books as a single unit, temporarily.  This one unit, combined with the remaining 25 books, can be arranged in
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document.write( "       (25+1)! = 26! ways
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document.write( "But for each one of these arrangements, the 5 math books can be arranged in 5! ways, therefore the total  is   
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document.write( "       26!*5!\r
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