Answer to Question #252639 in Discrete Mathematics for nurul

Question

There are 4 adults and 6 children sitting around a round table. If there must be at least one child

between any two adults, then

how many ways are there for them to sit around the table? Rotations are

considered the same, while reflections are distinct.

Answer 1

All ways 4 places can be taken for adults are presentated in the table below

Since table is round, then place number 10 is located next to place number 1

1 row is the number of place, places that occupated by adult marked with 1(others are occupated by kids)

All the other ways can be received from one of those by rotation.

Since there are 4 adults, then number of permutations within 4 places is equal to 4! = 24

The number of permutations for 6 kids within 6 places is equal to 6! = 720

The number of total ways is 24*720 = 17280