Seven different models cars, from which there are three blue and four red, are to be parked in a row. Find how many different ar

First, we should create a visual representation. I can do this by making a list, similar to a data set. Let b signify blue and r signify red.

(b, b, b, r, r, r, r)

Keep in mind, this is not necessarily the set order.

We can now adjust the order.

1. The first car is blue.

This part is already set!

2. The last car is blue.

We can swap the second blue car with the last red car.

(b, r, b, r, r, r, b)

3. The middle car is blue.

We can exchange the middle red car for the third blue car.

(b, r, r, b, r, r, b)

This setup adheres to the guidelines. It is one valid arrangement!

5. But we still have more to determine! We need to assess whether any additional arrangements are possible.

There are none. This is confirmed because there are only three blue cars, and three designated spots for these cars must occupy.

As a result, we cannot swap any colors without breaching the guidelines.

Final Answer: There is one possible arrangement of the lineup:

(b, r, r, b, r, r, b)

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