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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 1, 2024
 #1
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There are 4 children, which means there are 4! = 4 x 3 x 2 x 1 = 24 ways to seat the children.

There are also 4 adults, which means there are, again, 4! = 4 x 3 x 2 x 1 = 24 ways to seat the adults.

 

Now, we just have to do 24*24 = 576 since each arrangement of children can be met by 24 ways to arrange the adults.  

 

There are 576 ways to do this!

 

Thanks! :)

 Jun 1, 2024

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