document.write( "Question 254218: Six cups and saucers come in pairs: there are two cups and saucers which are red, two white, and two with stars on. If the cups are placed randomly onto the saucers (one each), find the probability
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Algebra.Com's Answer #186521 by Edwin McCravy(20055) $\"\"$ $\"About$

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Six cups and saucers come in pairs: there are two cups and saucers which are red, two white, and two with stars on. If the cups are placed randomly onto the saucers (one each), find the probability
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document.write( "To place them all successfully, there are two types\r\n" );
document.write( "of ways of placing them:\r\n" );
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document.write( "An example of 1st type  \r\n" );
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document.write( "Saucers       R   R   W   W   S   S\r\n" );
document.write( "Cups          W   W   S   S   R   R\r\n" );
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document.write( "Example of 2nd type\r\n" );
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document.write( "Saucers       R   R   W   W   S   S\r\n" );
document.write( "Cups          W   S   R   S   R   W\r\n" );
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document.write( "So we have to consider each type of choice.\r\n" );
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document.write( "For type 1 cases only.            \r\n" );
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document.write( "There are 4 ways to place the 1st red cup. Having done that,\r\n" );
document.write( "there is 1 way to place the 2nd red cup. Having done that,\r\n" );
document.write( "there are 2 ways to place the 1st white cup. Having done that,\r\n" );
document.write( "there is 1 way to place the 2nd white cup. Having done that,\r\n" );
document.write( "there are 2 ways to place the 1st starred cup. Having done that,\r\n" );
document.write( "there is 1 way to place the 2nd starred cup.\r\n" );
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document.write( "Therefore there are 4*1*2*1*2*1 or 16 ways to place the cups successfully\r\n" );
document.write( "in a configuration like Type 1.  \r\n" );
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document.write( "Example of 2nd type\r\n" );
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document.write( "Saucers       R   R   W   W   S   S\r\n" );
document.write( "Cups          W   S   R   S   R   W\r\n" );
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document.write( "For type 2 cases only:            \r\n" );
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document.write( "There are 4 ways to place the 1st red cup. Having done that,\r\n" );
document.write( "there are 2 ways to place the 2nd red cup. Having done that,\r\n" );
document.write( "there are 3 ways to place the 1st white cup. Having done that,\r\n" );
document.write( "there are 2 ways to place the 2nd white cup. Having done that,\r\n" );
document.write( "there are 2 ways to place the 1st starred cup. Having done that,\r\n" );
document.write( "there is 1 way to place the 2nd starred cup.\r\n" );
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document.write( "Therefore there are 4*2*3*2*2*1 or 96 ways to place the cups successfully\r\n" );
document.write( "in a configuration like Type 2.\r\n" );
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document.write( "So there are a total of 16 + 96 or 112 ways to place the\r\n" );
document.write( "cups successfully.\r\n" );
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document.write( "To place all the cups, regardless of whether successfully or unsuccesfully:\r\n" );
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document.write( "There are 6 ways to place the 1st red cup. Having done that,\r\n" );
document.write( "there are 5 ways to place the 2nd red cup. Having done that,\r\n" );
document.write( "there are 4 ways to place the 1st white cup. Having done that,\r\n" );
document.write( "there are 3 ways to place the 2nd white cup. Having done that,\r\n" );
document.write( "there are 2 ways to place the 1st starred cup. Having done that\r\n" );
document.write( "there is 1 way to place the 2nd starred cup.\r\n" );
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document.write( "Therefore there are 6*5*4*3*2*1 or 720 ways to place the cups any\r\n" );
document.write( "old way.\r\n" );
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document.write( "The probability is therefore  or \r\n" );
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document.write( "Edwin

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