A group of eight students have lockers that are arranged as shown, in two rows of four lockers with one row directly on top of the other. The students are allowed to paint their lockers either blue or red according to two rules. The first rule is that there must be two blue lockers and two red lockers in each row. The second rule is that lockers in the same column must have different colours. How many ways are there for the students to paint their lockers according to the rules?

![](https://cdn.mathpix.com/cropped/2024_04_17_587bc2a8915214d42f9eg-1.jpg?height=691&width=639&top_left_y=1758&top_left_x=800)
As soon as two lockers are painted blue in the top row, the other two lockers in the top row must be painted red.

Once the top row is painted, the colours of the lockers in the bottom row are determined.

If the lockers in the top row are numbered $1,2,3$, and 4 , then there are six possibilities for the two blue lockers.

They are 1 and 2, 1 and 3,1 and 4, 2 and 3,2 and 4, and 3 and 4.

ANSWER: 6