document.write( "Question 1150598: A bag contains three black balls, four white balls, and five red balls. Three
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Algebra.Com's Answer #771986 by Edwin McCravy(20056)\"\" \"About 
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document.write( "First we calculate the number of ways of removing any 3 balls from the 3+4+5=12\r\n" );
document.write( "balls. This is 12C3 = 220 ways to remove any 3 balls.\r\n" );
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document.write( "We first find the number of ways we don't want, which is the number of obtaining\r\n" );
document.write( "either no reds or just 1 red.\r\n" );
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document.write( "The number of ways of getting no reds is the number of ways of choosing 3 from\r\n" );
document.write( "the 3+4=7 non-red balls.  This is 7C3 = 35 ways.\r\n" );
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document.write( "The number of ways of getting exactly 1 red is the number of ways of: \r\n" );
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document.write( "1. choosing 2 from the 3+4=7 non-red balls.  This is 7C2 = 21 ways.\r\n" );
document.write( "and for each of these 21 ways,\r\n" );
document.write( "2. choosing the 1 red ball. This is 5C1 = 5 ways\r\n" );
document.write( "That's 21∙5 = 105 ways to get exactly 1 red ball.\r\n" );
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document.write( "So the total number of ways to get what we don't want is 35+105 = 140 ways.\r\n" );
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document.write( "That leaves 220-140=80 ways we want.\r\n" );
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document.write( "So the desired probability is 80 ways out of 220 or 80/220 which reduces to\r\n" );
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document.write( "4/11.\r\n" );
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document.write( "Edwin
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