document.write( "Question 1204839: There is a group of five children, where two of the children are twins. In how
\n" ); document.write( "many ways can I distribute 18 identical pieces of candy to the children, if the
\n" ); document.write( "twins must get 7 pieces of candy? \n" ); document.write( "

Algebra.Com's Answer #841394 by ikleyn(52793) $\"\"$ $\"About$

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\n" ); document.write( "There is a group of five children, where two of the children are twins. In how
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\n" ); document.write( "18 identical pieces of candy to the children, if the twins must get 7 pieces of candy?
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\n" ); document.write( "\n" ); document.write( "I came with third interpretation, which differs from that by Edwin's and @greenestamps.\r
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\n" ); document.write( "\n" ); document.write( "I will assume that\r
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\n" ); document.write( "\n" ); document.write( "    (1)   for twins and for other 5-2 = 3 children the distributions allow 0 pieces for some child/children
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\n" ); document.write( "             (but the sum of pieces for twins is always 7 and the sum of pieces for other three children is always 18-7 = 11)\r
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\n" ); document.write( "\n" ); document.write( "    (2)   The number of pieces each twin gets is IMPORTANT.\r
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\n" ); document.write( "\n" ); document.write( "So, my interpretation is half-way between that of Edwin and @greenestaps.\r
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\n" ); document.write( "\n" ); document.write( "In support of this interpretation, I should say following:\r
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document.write( "    (a)  My assumption (1) is inhumane; but this problem is not about humanitarian mission - it is about\r\n" );
document.write( "         solving Math problem as it is given.  So, I leave humanitarian reasons aside as irrelevant.\r\n" );
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document.write( "    (b)  My assumption (2) reflects the fact that the twins are two different distinguishable individuals;\r\n" );
document.write( "         therefore, when they obtain different numbers of pieces, it corresponds to different distinguishable distributions.\r\n" );
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\n" ); document.write( "\n" ); document.write( " After all these explanations, below is the solution itself.\r
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document.write( "So, for 3 children, I have the \"stars and bars\" distribution problem with n=3 persons and k=11 pieces, with 0 (zero)\r\n" );
document.write( "lower boundary of pieces for individuals.\r\n" );
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document.write( "For this 3 children, the number of possible distributions is  =  =  =  = 78.\r\n" );
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document.write( "For the twins, there are 7+1 = 8 different distributions (they correspond to  numbers {0,1,2,3,4,5,6,7} of pieces \r\n" );
document.write( "which one of the twins does obtain; then the other twin gets the rest of 7).\r\n" );
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document.write( "So, the ANSWER  to the problem is this product  8*78 = 624.\r\n" );
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\n" ); document.write( "\n" ); document.write( "This is my solution in my interpretation.\r
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