To solve this problem, we need to divide 8 children into two groups of 3 and one group of 2.

First, choose 3 children out of 8 for the first group: \(\binom{8}{3}\).

Next, choose 3 children out of the remaining 5 for the second group: \(\binom{5}{3}\).

The remaining 2 children automatically form the last group: \(\binom{2}{2}\).

The total number of ways is given by multiplying these combinations:

\(\binom{8}{3} \times \binom{5}{3} \times \binom{2}{2} = 56 \times 10 \times 1 = 560\).