document.write( "Question 1206887: How many different candy boxes with 6 candies of 5 sorts can be compounded?
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\n" ); document.write( " 5
\n" ); document.write( " 120
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Algebra.Com's Answer #844611 by ikleyn(52798) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "How many different candy boxes with 6 candies of 5 sorts can be compounded?
\n" ); document.write( "720
\n" ); document.write( "5
\n" ); document.write( "120
\n" ); document.write( "6
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document.write( "So, we want to have 6 candies in a box compounded of 5 different sorts.\r\n" );
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document.write( "Now, the most simple reading/interpretation is that the order of these 6 candies \r\n" );
document.write( "in the box does not matter.\r\n" );
document.write( "At least, it is so from the point of view of any child :)\r\n" );
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document.write( "If so, then we should have all 5 candies in the box of different sorts,\r\n" );
document.write( "PLUS the 6-th candy of some sort.\r\n" );
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document.write( "So, for us the only question does matter: which of 5 possible sorts of candies is doubled?\r\n" );
document.write( "It makes clear that the answer to the problem's question is 5  (in this problem's reading).\r\n" );
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document.write( "I am 97% sure that it is the correct reading (and, correspondingly, a correct answer), \r\n" );
document.write( "and it is the reading and the answer which is expected in this problem.\r\n" );
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document.write( "But formally, there is a small percentage opportunity for another reading and another\r\n" );
document.write( "solution, which follows below.\r\n" );
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document.write( "This another reading says that there are 5 different letters A, B, C, D and E, that correspond \r\n" );
document.write( "to 5 sorts of candies, and the question is how many possible arrangements (6-letter words) \r\n" );
document.write( "can be written in this 5-letter alphabet so that all 5 letters are used.\r\n" );
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document.write( "So, in this problem there are 6! = 720 permutations, in all, but we should consider only 720/2 = 360 \r\n" );
document.write( "of them as distinguished arrangements, since each permutation has one and only one letter doubled,\r\n" );
document.write( "and the doubled letter produces only one arrangement from two possible permutations.\r\n" );
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document.write( "It is the second possible (3 percent of possibility) interpretation, the solution and the answer.\r\n" );
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document.write( "So, in first interpretation the answer is :  there are 5 different candy boxes (pointing only coinciding sorts of candies).\r\n" );
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document.write( "In the second interpretation, the answer is :  there are 360 distinguishable boxes/arrangements.\r\n" );
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document.write( "But not 720, as in the solution by @Theo, which is incorrect.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "The notice for readers and for a composer: this problem is written unprofessionally
\n" ); document.write( "and can not be considered as 100% clean/clear accurate Math problem, since it does not define,
\n" ); document.write( "which boxes are considered as equivalent (or identical), and which boxes are considered as different.\r
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