Question

Joseph has got a toy car, a teddy bear, a ball and a ship. he wants to put them in a new order on the shelf. the ship must be next ot the car, and the teddy bear should also be next to the car. in how many different orders can put the toys on the shelf?

Answer 1

Joseph can arrange his four toys on the shelf in 4 different orders, taking into account that the ship and the teddy bear must be next to the car.

Step-by-step explanation:

The student is asking about the number of different orders Joseph can arrange his four toys on a shelf with specific conditions: the ship must be next to the car, and the teddy bear must also be next to the car. To solve this, consider the car as the central piece, since both the ship and the teddy bear must be next to it. We can treat the car-ship and car-teddy bear as single units, as these pairs can't be separated. Now, there are two options: either the ship is on the left side of the car or on the right side, and the same goes for the teddy bear.

Step 1: Choose the side for the ship and teddy bear. There are two choices: the ship and teddy bear can either be on the left or the right of the car. When one is chosen, the other side is automatically decided for the other toy. Therefore we have 2 options here.

Step 2: Now that the ship and teddy bear are arranged, we still have two toys to arrange, the car-ship or the car-teddy bear as one unit, and the ball. These two items can be arranged in 2! (2 factorial) ways, which is 2 x 1 = 2.

Step 3: Multiply the number of ways to arrange the ship and teddy bear (Step 1) by the number of ways to arrange the remaining toys (Step 2): 2 x 2 = 4.

Therefore, Joseph can arrange his toys in 4 different orders on the shelf based on the given conditions.