To solve this problem, we need to consider the number of ways each child can choose their scoop of ice cream while ensuring that exactly three children choose the same flavor.
Step 1: Select the flavor that will be chosen by three children.
Since we have 3 flavors available, we can choose one of them in C(3, 1) = 3 ways.
Step 2: Distribute the remaining flavors to the remaining children.
Now we have 5 children left and 2 flavors remaining. We need to distribute these flavors among the children. To do this, we can use a technique called stars and bars. We can think of each flavor as a "star" and the spaces between the children as "bars".
For example, if we have 5 children and 2 flavors, one possible distribution would be:
*|**|*|**|
In this case, the first child gets no scoop, the second and fifth children get the first flavor, and the third and fourth children get the second flavor.
The number of ways to distribute the remaining flavors is given by C(5+2-1, 2-1) = C(6, 1) = 6.
Step 3: Multiply the results from step 1 and step 2.
To find the total number of ways, we multiply the results from step 1 and step 2 together: 3 * 6 = 18.
Therefore, there are 18 ways in which each child can choose a flavor for their scoop of ice cream so that exactly three children choose the same flavor.