document.write( "Question 252231: A bag contains six small straws of the following lengths: 2 cm, 3 cm, 5 cm, 7 cm, 11 cm, 13 cm Three straws are drawn at random. What is the probability that a triangle can be formed with the straws that are drawn?\r
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Algebra.Com's Answer #184076 by Edwin McCravy(20055) $\"\"$ $\"About$

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A bag contains six small straws of the following lengths: 2 cm, 3 cm, 5 cm, 7 cm, 11 cm, 13 cm Three straws are drawn at random. What is the probability that a triangle can be formed with the straws that are drawn?
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document.write( "To form a triangle, every pair of the three straws drawn \r\n" );
document.write( "must have lengths whose sum is greater than the third side.\r\n" );
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document.write( "If we choose the longest two straws, 13cm and 11cm,\r\n" );
document.write( "the third straw can be 3cm, 5cm or 7cm.  So that's 3\r\n" );
document.write( "successful choices.\r\n" );
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document.write( "If we choose the longest and the next to the longest,\r\n" );
document.write( "13cm and 7cm, neither 5cm nor 3cm nor 2cm will form a triangle.\r\n" );
document.write( "So we still have only 3 successful choices.\r\n" );
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document.write( "So that's all the ways we can choose the 13 cm straw\r\n" );
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document.write( "If we choose the 11cm and 7cm, then we can only choose \r\n" );
document.write( "the 5cm.  So that's another way.  So far we now have \r\n" );
document.write( "4 successful choices.  That's all the ways we can\r\n" );
document.write( "include the longest two.\r\n" );
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document.write( "There is just one more successful choice with 7cm being \r\n" );
document.write( "the longest, namely the 5cm and the 3cm.  So that makes \r\n" );
document.write( "5 ways in all. \r\n" );
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document.write( "So there are only five successful choices of three so that the \r\n" );
document.write( "sum of every pair of straw's lengths is greater than the third\r\n" );
document.write( "straw's length.  They are \r\n" );
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document.write( "1. 13,11,7 cm\r\n" );
document.write( "2. 13,11,5 cm\r\n" );
document.write( "3. 13,11,3 cm\r\n" );
document.write( "4. 11,7,5 cm\r\n" );
document.write( "5. 7,5,3 cm\r\n" );
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document.write( "There are  ways to draw any three straws.\r\n" );
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document.write( "So the desired probability is  or , choice (e).\r\n" );
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document.write( "Edwin

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