According to the requirements, the first category must be one of liberal arts or science. If the first class is science, it must be liberal arts-science-liberal arts-science-liberal arts. The same is true for the first category, so there are two ways to choose arts and sciences.

Then liberal arts and science are different elements respectively. After the first category is determined, the two subjects should be filled separately. After the first category is selected, the respective positions of liberal arts and science are determined, which are 3x2x 1=6, so:

There are 2x6x6=72 species in total.

Two common basic counting principles of permutation and their applications;

1, addition principle sum classification counting method;

Each method in each class can accomplish this task independently. The specific methods in the two different methods are different from each other (that is, the classification is not heavy). Any method to accomplish this task belongs to a certain category (that is, classification does not leak).

2. Multiplication principle and step counting method:

One method of any step can't accomplish this task, and only by continuously completing these N steps can this task be accomplished. Every step is independent of each other. As long as the methods used in a step are different, the corresponding methods to complete it are also different.