Question

школьники из волгограда собрались на каникулы поехать в москву, посетив по дороге нижний новгород. сколькими различными способами могут ребята осуществить свое путешествие, если из волгограда в нижний новгород можно отправиться на теплоходе или поезде, а из нижнего новгорода в москву- на самолете, теплоходе или автобусе? решите задачу с помощью построения дерева

Answer 1

восемь способов.
напиши города и соедини их прямыми, волгоград 2 прямые в н.н, из н.н. 4 прямые в м. получишь дерево

Answer 2

Problem Analysis

The problem states that a group of schoolchildren from Volgograd plans to travel to Moscow for their vacation, with a stop in Nizhny Novgorod along the way. They have the option to travel from Volgograd to Nizhny Novgorod by either boat or train, and from Nizhny Novgorod to Moscow by plane, boat, or bus. The task is to determine how many different ways the children can make their journey.

Solution

To solve this problem, we can use a tree diagram to visualize the different paths the children can take. Each level of the tree represents a different leg of the journey, and the branches represent the different modes of transportation available.

Let's construct the tree diagram step by step:

1. Start with the root node representing the starting point, Volgograd. 2. Create two branches from the root node for the two options to travel to Nizhny Novgorod: boat and train. 3. From each Nizhny Novgorod node, create three branches for the three options to travel to Moscow: plane, boat, and bus.

The tree diagram will have a total of 6 leaf nodes, representing the different ways the children can complete their journey.

Tree Diagram

Here is the tree diagram representing the different ways the children can travel:

Volgograd
├── Boat
│   ├── Plane
│   ├── Boat
│   └── Bus
└── Train
    ├── Plane
    ├── Boat
    └── Bus

Counting the Paths

By examining the tree diagram, we can see that there are 6 different paths the children can take to travel from Volgograd to Moscow via Nizhny Novgorod:

1. Volgograd -> Boat -> Plane -> Moscow 2. Volgograd -> Boat -> Boat -> Moscow 3. Volgograd -> Boat -> Bus -> Moscow 4. Volgograd -> Train -> Plane -> Moscow 5. Volgograd -> Train -> Boat -> Moscow 6. Volgograd -> Train -> Bus -> Moscow

Therefore, the schoolchildren can travel in 6 different ways to reach Moscow, including their stop in Nizhny Novgorod.

Conclusion

The schoolchildren from Volgograd can travel to Moscow, with a stop in Nizhny Novgorod, in 6 different ways. These include traveling by boat or train from Volgograd to Nizhny Novgorod, and then by plane, boat, or bus from Nizhny Novgorod to Moscow.

Please note that the tree diagram and the counting of paths were done manually based on the given information.