Question

Seven different models cars, from which there are three blue and four red, are to be parked in a row. Find how many different arrangements there are if the first, the last, and the car in the middle of the queue should be blue.
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Answer 1

First, we need to make a visual. I can do this by making a list, like in a data set. Let b = blue and r = red.

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

Note that this is not necessarily the order.

Now we can modify the order.

1. The first car is blue

This is already done!

2. The last car is blue.

We can trade the second blue with the last red.

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

3. The middle car is blue.

We can trade the middle red with the third blue.

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

This arrangement we have created follows the rules. It is one possible queue!

5. But we aren't done yet! We need to figure out if there are any more arrangements.

There is none. We know this because there are only three cars that are blue, and three spots these cars MUST park in.

Therefore, we could not swap any colors without maintaing the rules.

Answer: There is one possible arrangement of the queue:

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

Please let me know if this was helpful, or if you have any questions. If you have time, I'd be so grateful for a rating!