document.write( "Question 1122445: Paige Turner loves finite mathematics. She has 5 books about probability and 4 books about matrices. Her friend Anita Tudor wants to borrow four of these books. \r
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\n" ); document.write( "\n" ); document.write( "b) there are two books on each topic (i.e. two matrix books and two probability books)? \r
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Algebra.Com's Answer #738579 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Paige Turner loves finite mathematics. She has 5 books about probability and 4 books about matrices. Her friend Anita Tudor wants to borrow four of these books. \r
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document.write( "9 books CHOOSE 4 = 9C4 = (9∙8∙7∙6)/(4∙3∙2∙1) = 3024/24 = 126 ways\r\n" );
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\n" ); document.write( "b) there are two books on each topic (i.e. two matrix books and two probability books)?
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document.write( "(5 probability books CHOOSE 2) AND (4 matrix books CHOOSE 2) = (5C2)∙(4C2) =\r\n" );
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document.write( "[(5∙4)/(2∙1)]∙[(4∙3)/(2∙1)] = [20/2]∙[12/2] = 10∙6 = 60 ways\r\n" );
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\n" ); document.write( "c) there is at least one book on each topic?
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document.write( "Whenever we see the words \"at least\", we proceed in two steps:\r\n" );
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document.write( "1. Find the number of ways to select ANY 4 books.\r\n" );
document.write( "2. Find the total number of UNWANTED selections of 4 books.\r\n" );
document.write( "3. Subtract the second number from the first.\r\n" );
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document.write( "1. This was the answer to part (a) with no restrictions, or 126 ways\r\n" );
document.write( "2. There are two types of UNWANTED selections, so we will have to calculate\r\n" );
document.write( "   both types of UNWANTED selections.  The 2 types of unwanted selections\r\n" );
document.write( "      are:\r\n" );
document.write( "   A. When all 4 books are probability books and there are no matrix books.\r\n" );
document.write( "   B. When all 4 books are matrix books and there are no probability books.\r\n" );
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document.write( "   A. That's 5 probability books CHOOSE 4 = 5C4 = (5∙4∙3∙2)/(4∙3∙2∙1) =\r\n" );
document.write( "      120/24 = 5 ways\r\n" );
document.write( "   B. That's 4 matrix books CHOOSE 4 = 4C4 = (4∙3∙2∙1)/(4∙3∙2∙1) =\r\n" );
document.write( "      24/24 = 1 way   \r\n" );
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document.write( "So the total number of UNWANTED ways is 5+1 or 6\r\n" );
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document.write( "3. Subtract 6 from 126 and get 126-6 = 120.\r\n" );
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document.write( "Edwin
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