document.write( "Question 1204253: (a) Find the number of ways that Magnus can give out 12 identical stickers to 12 of his friends. (Not everyone has to get a sticker.)\r
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Algebra.Com's Answer #840385 by ikleyn(52944) $\"\"$ $\"About$

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(a) Find the number of ways that Magnus can give out 12 identical stickers
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document.write( "                 Part (a)\r\n" );
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document.write( "In this problem, stickers are not distinguishable, but the friends are.\r\n" );
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document.write( "This problem is equivalent to the question: how many solutions does this equation have\r\n" );
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document.write( "     +  +  + . . . +  = n\r\n" );
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document.write( "in integer non-negative numbers at n= 12, k= 12 ?\r\n" );
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document.write( "The answer is: the number of such solutions is  =  =  = 1352078.\r\n" );
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document.write( "This formula is deduced using so called \"stars and bars method\".\r\n" );
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document.write( "On \"stars and bars method\", see this Wikipedia article \r\n" );
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document.write( "https://en.wikipedia.org/wiki/Stars_and_bars_%28combinatorics%29\r\n" );
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document.write( "or read from my lesson\r\n" );
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document.write( "    - Stars and bars method for Combinatorics problems \r\n" );
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document.write( "in this site.\r\n" );
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document.write( "                 Part (b)\r\n" );
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document.write( "This problem means that each friend gets exactly one sticker.\r\n" );
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document.write( "And since the stickers are undistinguishable, it means that there is only one scenario \r\n" );
document.write( "to distribute stickers in a way, as it is assigned by the problem.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Does the answer to (b) seem to be unexpected ?     Did you expect to get the answer 12! ? \r
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\n" ); document.write( "\n" ); document.write( "        Remember that 12! relates to permutations of 12 different items,
\n" ); document.write( "        while in this problem all the stickers are identical.\r
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\n" ); document.write( "\n" ); document.write( "This problem teaches you to read the problem attentively.\r
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