Question
MODELING REAL LIFE A train has one engine and six train cars.
Find the total number of ways an engineer can arrange the train.
(The engine must be first.)
There are
Find the total number of ways an engineer can arrange the train.
(The engine must be first.)
There are
Ask by Fowler Powell. in the United States
Mar 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
There are 720 total ways to arrange the train.
Solution
- Since the engine is fixed as the first car, the remaining six train cars can be arranged in any order.
- The number of arrangements for the six train cars is given by the factorial of 6, which is
- Therefore, there are
total ways to arrange the train.
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When arranging the train with one engine followed by six train cars, the engine’s position is fixed at the front. Therefore, we only need to arrange the six train cars, which can be ordered in
This scenario is a classic example of permutations, where the order matters. If you have different types of train cars (like passenger cars, freight cars, etc.), you’d need to factor in any restrictions or specific arrangements desired. But in this case, just six unique cars give you a straightforward
