Question

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.)

Answer 1

Answer:

720

Step-by-step explanation:

i dont really know how but i saw on a different answer that you just have to multiply from highest number down to 1

ex: 6 x 5 x 4 x 3 x 2 x 1

Answer 2

The total number of ways that six cars can be arranged is 720

Given:

A train has one engine and six train cars.

To find:

Find the total number of ways an engineer can arrange the train.

(The engine must be first.)  

Solution:

From the data,

A train has one engine and six train cars  

It given that first must the engine  

Hence, remaining places = (7 - 1) = 6

Now the different ways can be arranged in 6 places  

Number of ways that 6 cars can be arranged in 1st place = 6

One place is occupied,

Number of ways that 5 cars can be arranged in 2nd place = 5

Since 2 places are occupied,

Number of ways that 4 cars can be arranged in 3rd place = 4

Similarly,

Number of ways that 3 cars can be arranged in 4th place = 3  

Number of ways that 2 cars can be arranged in 5th place = 2  

Number of ways that 1 car can be arranged in 6th place = 1

Hence,

Total number of ways = 6 × 5 × 4 × 3 × 2 × 1 = 720

Therefore,

The total number of ways that six cars can be arranged is 720

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