Final answer:
To ensure each flavor of ice cream is selected by at least one child, we need to use combinations to distribute the flavors amongst the children. The formula C(n + r - 1, r) can be used to calculate the number of ways to do this, where n is the number of flavors and r is the number of children. In this case, there are 3 flavors of ice cream and 6 children, resulting in 28 possible combinations.
Step-by-step explanation:
To solve this problem, we can use the concept of combinations. Since there are 3 flavors of ice cream and 6 children, each child needs to choose a flavor. In order for each flavor to be selected by at least one child, we need to distribute the flavors among the children in such a way that no flavor is left out.
One possible way to solve this is to think of it as a stars and bars problem. We can imagine the 3 flavors of ice cream as 3 distinct objects, and the 6 children as 6 bins. We need to distribute the 3 flavors among the 6 children, ensuring that each child gets at least one flavor.
The number of ways to do this is given by the formula C(n + r - 1, r), where n is the number of flavors and r is the number of children. In this case, n = 3 and r = 6, so the number of ways to distribute the flavors is C(3 + 6 - 1, 6) = C(8, 6) = 28.
Therefore, there are 28 ways for each child to choose a flavor of ice cream such that each flavor is selected by at least one child.