How many ways can 3 cars and 4 trucks be selected from 9 cars and 5 trucks to be tested for a safety inspection? There are ways to select the cars and trucks for the safety inspection.

Step 1 ：This problem is about selecting a certain number of items (cars and trucks) from a larger set (all the cars and trucks available). The order in which we select the items does not matter, so this is a combination problem.

Step 2 ：The formula for combinations is \(C(n, k) = \frac{n!}{k!(n-k)!}\), where n is the total number of items, k is the number of items to select, and ! denotes factorial, which is the product of all positive integers up to that number.

Step 3 ：We need to calculate the number of ways to select 3 cars from 9, and 4 trucks from 5. These are independent events, so we multiply the two results together to get the total number of ways to select the vehicles for the safety inspection.

Step 4 ：Calculating the combinations, we find that there are 84 ways to select the cars and 5 ways to select the trucks.

Step 5 ：Multiplying these together, we find that there are \(84 \times 5 = 420\) ways to select the cars and trucks for the safety inspection.

Step 6 ：Final Answer: \(\boxed{420}\)