In how many ways can a person order one ice cream cone with 3 different flavors of ice cream if there are 19 flavors to choose from and it matters to the person how the 3 flavors are stacked on the one cone? That is, which flavor is on the top, middle, and bottom. There are possible ways to order the ice cream cone.

Step 1 ：We are given a problem where a person can order one ice cream cone with 3 different flavors of ice cream. There are 19 flavors to choose from and the order in which the flavors are stacked on the cone matters.

Step 2 ：This is a permutation problem because the order of the flavors matters. The formula for permutations is \(nPr = \frac{n!}{(n-r)!}\), where \(n\) is the total number of items to choose from, \(r\) is the number of items to choose, and \(!\) denotes factorial.

Step 3 ：In this case, \(n\) is 19 (the number of ice cream flavors) and \(r\) is 3 (the number of flavors to choose for the cone).

Step 4 ：Substituting the given values into the permutation formula, we get \(19P3 = \frac{19!}{(19-3)!}\).

Step 5 ：Calculating the above expression, we find that there are 5814 different ways to order the ice cream cone.

Step 6 ：Final Answer: The number of ways to order the ice cream cone with 3 different flavors out of 19 is \(\boxed{5814}\).