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(52781)![]() ![]() You can put this solution on YOUR website! . \n" ); document.write( " \r\n" ); document.write( "\r\n" ); document.write( "As I understand/interpret this problem, there are 8 + 5 + 3 = 16 items, in all.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "Of them, 8 platters are identical (indistinguishable; cookies, letter C);\r\n" ); document.write( "\r\n" ); document.write( " 5 other platters are identical (indistinguishable; fruits, letter F);\r\n" ); document.write( "\r\n" ); document.write( " 3 other platters are identical (indistinguishable; pies, letter P).\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); 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" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "Same as to ask how many distinguishable words of the length 16 can be arranged having 8 identical letters C; \r\n" ); document.write( "\r\n" ); document.write( "5 identical letters F and 3 identical letters P.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "The answer is\r \n" ); document.write( "\n" ); document.write( "Solved.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "There is NOTHING IN COMMON with the solution by @ewatrrr.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "----------------\r \n" ); document.write( " \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 \n" ); document.write( "\n" ); document.write( "in this site.\r \n" ); document.write( " \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 \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic \"Combinatorics: Combinations and permutations\". \r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r \n" ); document.write( " \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 \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |