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# Counting

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Four children and four adults are to be seated at a circular table.  In how many different ways can they be seated if all the children are next to each other, and all the adults are next to each other?  (Two seatings are considered the same if one can be rotated to form the other.)

Jun 20, 2024

#1
+1230
+1

First, let's calculate the number of ways to sit each group.

There are 4 children. We can arrange them in \(4! = 4*3*2*1=24\) ways.

Then, there are 4 parents. We can arrange them in \(4! = 4*3*2*1=24\) ways.

For every one arrangment of adults, there are 24 ways to arrange children, so we have

\(24*24=576\)

Let me know if I messed up, my counting is not the best.

Thanks! :)

Jun 20, 2024

#1
+1230
+1

First, let's calculate the number of ways to sit each group.

There are 4 children. We can arrange them in \(4! = 4*3*2*1=24\) ways.

Then, there are 4 parents. We can arrange them in \(4! = 4*3*2*1=24\) ways.

For every one arrangment of adults, there are 24 ways to arrange children, so we have

\(24*24=576\)