document.write( "Question 1142526: Ten people are to be seated at two circular tables. One table seats six people and the other seats four. \r
\n" ); document.write( "\n" ); document.write( "i) With these tables, how many different seating arrangements are there for the ten people?\r
\n" ); document.write( "\n" ); document.write( "ii) Assuming that the seating is random, what is the probability that a particular couple will be seated at the same table?\r
\n" ); document.write( "\n" ); document.write( "Thank you in advance! I'm not really great at perms and comms questions. If you could include an explanation in words, I would realy appreciate it :) \n" ); document.write( "

Algebra.Com's Answer #763215 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "(i)  First, you can select 6 persons from 10 people by  \r\n" );
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document.write( "           ways =  ways = 210 ways\r\n" );
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document.write( "     to seat them around the first table.  Then the team for the second table will be the rest (without further choice).\r\n" );
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document.write( "     Second, you can arrange 6 people around the first circular table by   = 5! ways = 120 ways  \r\n" );
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document.write( "     (using this standard well known formula).\r\n" );
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document.write( "     Third, you can arrange 4 people around the second circular table by   = 3! ways = 6 ways.\r\n" );
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document.write( "     Finally, the answer to the problem's question is this product\r\n" );
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document.write( "         210*120*6 = 151200 ways.      ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "To expand your knowledge about combinations and permutations, look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Introduction to Permutations\r
\n" ); document.write( "\n" ); document.write( "    - PROOF of the formula on the number of Permutations\r
\n" ); document.write( "\n" ); document.write( "    - Problems on Permutations\r
\n" ); document.write( "\n" ); document.write( "    - Introduction to Combinations\r
\n" ); document.write( "\n" ); document.write( "    - PROOF of the formula on the number of Combinations\r
\n" ); document.write( "\n" ); document.write( "    - Problems on Combinations\r
\n" ); document.write( "\n" ); document.write( "    - Arranging elements of sets containing indistinguishable elements \r
\n" ); document.write( "\n" ); document.write( "    - Persons sitting around a cicular table (*)\r
\n" ); document.write( "\n" ); document.write( "    - Combinatoric problems for entities other than permutations and combinations \r
\n" ); document.write( "\n" ); document.write( "    - Miscellaneous problems on permutations, combinations and other combinatoric entities \r
\n" ); document.write( "\n" ); document.write( "    - In how many ways N distinguishable objects can be distributed among n different boxes ? \r
\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on Permutations and Combinations\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "A convenient place to quickly observe these lessons from a \"bird flight height\" (a top view) is the last lesson in the list.\r
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\n" ); document.write( "\n" ); document.write( "The most relevant lesson in the list is marked by (*).\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 lessons are the part of this online textbook under the topic \"Combinatorics: Combinations and permutations\". \r
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\n" ); document.write( "
\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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