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Help with this counting plz

 

Three adults and three children are to be seated at a circular table.  In how many different ways can they be seated if each child must be next to at least one adult?  (Two seatings are considered the same if one can be rotated to form the other.)

 Jan 31, 2023
 #2
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You need to draw the table and put the people in follow what I am saying.

 

Put a particular child at the head of the table. that child represents the head of the table so roation has already been accounted for.

 

Now you can have an adult on each side of this child then the other child adults places are set.   

3! arrangements for adults, 2 arrangements for children = 3!*2 = 12

 

or

 

You can have an adult on one side and a child on the other side  then the other A/C are set

3! * 2 = 12

 

Total = ?

 Jan 31, 2023

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