document.write( "Question 1175410: A caterer is arranging a row of desserts. The row will contain 8 platters of cookies, 5 trays of fruit, and 3 pies. In how many distinct ways can the cookies, fruit, and pies, be arranged in a row, if each type of desert is of the same kind? \n" ); document.write( "
Algebra.Com's Answer #801024 by ikleyn(52784)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "As I understand/interpret this problem, there are 8 + 5 + 3 = 16 items, in all.\r\n" );
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document.write( "Of them, 8 platters are identical (indistinguishable; cookies, letter C);\r\n" );
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document.write( "         5 other platters are identical (indistinguishable; fruits, letter F);\r\n" );
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document.write( "         3 other platters are identical (indistinguishable; pies, letter P).\r\n" );
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document.write( "The question is, how many distinguishable arrangements of these letters/items\r\n" );
document.write( "of the length 16 can be made ?\r\n" );
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document.write( "Same as to ask how many distinguishable words of the length 16 can be arranged having 8 identical letters C; \r\n" );
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document.write( "5 identical letters F  and  3 identical letters P.\r\n" );
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document.write( "The answer is  \"16%21%2F%288%21%2A5%21%2A3%21%29\" = \"%2816%2A15%2A14%2A13%2A12%2A11%2A10%2A9%29%2F%28%281%2A2%2A3%2A4%2A5%29%2A%281%2A2%2A3%29%29\" = 720720.     \r\n" );
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\n" ); document.write( "\n" ); document.write( "There is  NOTHING  IN  COMMON  with the solution by  @ewatrrr.\r
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\n" ); document.write( "\n" ); document.write( "To see other similar solved problems,  look into the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Arranging elements of sets containing indistinguishable elements \r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic  \"Combinatorics: Combinations and permutations\". \r
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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