SOLUTION: Traditional Chinese banquets consist of many round tables seating 10 persons.
How many different seating combinations are there for seating 20 people around two round tables.
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How many different seating combinations are there for seating 20 people around two round tables.
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Question 971260: Traditional Chinese banquets consist of many round tables seating 10 persons.
How many different seating combinations are there for seating 20 people around two round tables.
Assume that the tables are identical and indistinguishable, and the only thing that matters is the seating order around the table (in other words, each set position is also identical and indistinguishable from each other)
You can put this solution on YOUR website! Traditional Chinese banquets consist of many round tables seating 10 persons.
How many different seating combinations are there for seating 20 people around
two round tables.
Assume that the tables are identical and indistinguishable, and the only thing
that matters is the seating order around the table (in other words, each set
position is also identical and indistinguishable from each other)
Two seating arrangements are considered identical (indistinguishable) if each
person has the same person sitting to their immediate right and the same person
sitting to their immediate left.
There are 20 chairs. The twenty people can sit in the 20 chairs in 20! ways.
But we must now eliminate from that 20! the number of times each
indistinguishable arrangement is counted as distinguishable.
To do that we must divide 20! by:
1. The 10 ways we can rotate the 1st table, (so that each of the 10 people face
due north), since we consider those indistinguishable.
2. The 10 ways we can rotate the 2nd table, as in 1.
3. The 2 ways we can swap the 1st and 2nd tables, since we consider them
indistinguishable.
Answer = 12164510040883200 ways
Edwin
