Question

9 people sit around 1 rectangular table and 1 circular table.each table has 6 identical seats,other table is occupied only if the first table is fully occupied.how many arrangements are possible?

Answer 1

Each table has 6 identical seats and other table will be occupied only when the 1st table is fully occupied.

So the occupied seats on the 2nd table will be 3 in any case.

Now if 6 people sit around Rectangular table and 3 people sit around circular table , then

Number of arrangements = (6 - 1 )! . ( 3 -1 )!

                                          = 5! . 2!

                                          = 120 ( 2)

                                          = 240

Also

Now if 6 people sit around circular table and 3 people sit around Rectangular table ,

then

Number of arrangements = (6 - 1 )! . ( 3 -1 )!

                                          = 5! . 2!

                                          = 120 ( 2)

                                          = 240

So total number of arrangements = 240 + 240 = 480