how to calculate number of states for this logistics problem? Consider a logistics problem with 3 cities, 5 trucks and 3 packages. Each truck can be at any of the locations. A package can either be at one of the locations or in one of the trucks. What would the number of states be if an atomic representation is used? would the answer be 5 (num of trucks) x 3 (num of cities) x 3 ^ 8 (packages can be in a city or a truck) x 8? I feel like this is completely wrong. Can anyone give me a breakdown on how to solve these types of problems? Thank you

For each truck, there are 3 possible cities. This gives $3^5$ possibilities. Similarly, there are $5 + 3 = 8$ possibilities for each package. This gives $8^3$ possibilities. Thus, altogether, there are $3^5 \times 8^3$ possibilities.