Final answer:
The five Smith children can line up to order ice cream in 120 different ways, calculated by the factorial of the number of children, which is 5! or 120.
Step-by-step explanation:
The question asks about the number of ways the five Smith children can line up to order ice cream. This is a problem of counting arrangements or permutations. Assuming that each child is unique, the number of ways to arrange n items is given by n! (n factorial), where n factorial represents the product of all positive integers up to n.
For the Smith children, n is 5 because there are 5 children. Therefore, the number of ways they can line up is:
5! = 5 × 4 × 3 × 2 × 1 = 120
So, there are 120 different ways for the five Smith children to line up to order ice cream.