How many ways can  cars and  trucks be selected from  cars and  trucks to be tested for a safety inspection?

To solve this problem, we need to determine how many ways a certain number of cars and trucks can be selected from a larger group of cars and trucks.

Let:
- \( n_C \) represent the total number of cars,
- \( n_T \) represent the total number of trucks,
- \( k_C \) represent the number of cars to be selected,
- \( k_T \) represent the number of trucks to be selected.

The number of ways to select \( k_C \) cars from \( n_C \) cars is given by the combination formula:

\[
\binom{n_C}{k_C} = \frac{n_C!}{k_C!(n_C - k_C)!}
\]

Similarly, the number of ways to select \( k_T \) trucks from \( n_T \) trucks is:

\[
\binom{n_T}{k_T} = \frac{n_T!}{k_T!(n_T - k_T)!}
\]

To find the total number of ways to select both cars and trucks, we multiply the two combinations:

\[
\text{Total Ways} = \binom{n_C}{k_C} \times \binom{n_T}{k_T}
\]

If you provide the specific numbers for \( n_C \), \( n_T \), \( k_C \), and \( k_T \), I can calculate the exact number of ways.

Would you like to share the values so I can continue?

How many ways can cars and trucks be selected from cars and trucks to be tested for a safety inspection?

Discover how to calculate the number of ways to select cars and trucks for a safety inspection using the combination formula. This problem explores the core concepts of combinatorics, including selecting groups from larger sets. Suitable for high school students (Grades 9-12).

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