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There are 4 adults and 6 children. Adults can be arranged in (4-1)!=3!=6ways.
Out of the 6 children, at least 1 can sit between 2 adults. For this case, the maximum number of children who can sit between 2 adults is 2. Therefore, to determine the total number of ways for at least 1 child to sit between 2 adults we shall add as shown below,
Number of ways to arrange the children is .
Now the total number of ways is 6*21=126ways
Therefore, there are 126 ways for them to sit around the table.