document.write( "Question 1196897: Bailey the dog owns 8 balls. 4 are colored red, 3 are colored yellow, and 1 is blue. If she fetches 3 balls from her collection, how many different color combinations are possible? \n" ); document.write( "

Algebra.Com's Answer #829937 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "The problem asks about the number of different color combinations.\r\n" );
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document.write( "It means that we distinct the balls only due to their colors - \r\n" );
document.write( "- the balls with identical color are indistinguishable.\r\n" );
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document.write( "So, the math model is the set of all possible 3-letter words written \r\n" );
document.write( "using the alphabet consisting of 3 letter \r\n" );
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document.write( "    R (symbolizing red    color), \r\n" );
document.write( "    Y (            yellow color) and \r\n" );
document.write( "    B (            blue color)\r\n" );
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document.write( "with the restriction that the letter B can be used not more than once in each word.\r\n" );
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document.write( "    |   First consider the case when B is used exactly once in the words. | \r\n" );
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document.write( "If the order of colors is important, then the number of such words \r\n" );
document.write( "(different color combinations) with one B is 3*X*Z, \r\n" );
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document.write( "    where X can be any of R or Y, without restrictions\r\n" );
document.write( "      and Z can be any of R or Y, without restrictions.\r\n" );
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document.write( "The factor 3 symbolize that \"B\" may stand in any of three position in the word.\r\n" );
document.write( "So, the number of such words (different color combinations) with one B is 3*2*2 = 12,\r\n" );
document.write( "if the order of colors is important.\r\n" );
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document.write( "If the order of colors is not important, then all possible color combinations with one B are\r\n" );
document.write( "BRR, BRY, BYY, giving only 3 combinations.\r\n" );
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document.write( "    |   Next consider the case when B is NOT used in the words.  |\r\n" );
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document.write( "Then, if the order of colors is important, we can have any of two remaining colors \r\n" );
document.write( "in each position, giving 2*3 = 6 different color combinations.\r\n" );
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document.write( "If the order of colors is not important, then we have these combinations\r\n" );
document.write( "RRR, RRY, RYY, YYY, giving 4 possible color combinations.\r\n" );
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document.write( "ANSWER.  The number of all different color combinations is\r\n" );
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document.write( "               12 + 6 = 18, if the order is important;\r\n" );
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document.write( "                3 + 4 =  7, if the order is not important.\r\n" );
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