Determine the arrangement in two steps.

The first step is to determine the order of the four students.

This is a four-level full permutation with a (4,4) = 4 * 3 * 2 *1permutation.

The second step is to determine the position of the teacher.

There is no teacher at both ends of the question, so the teacher can only insert blank lines between the students.

Four students work in pairs.

And any two teachers are not even lined up together, * * * has three teachers,

Therefore, there can only be one teacher in each space.

There are three teachers for the three vacancies, and the arrangement is a (3,3) = 3 * 2 *1.

The final answer is A: A (4,4 4) * A (3 3,3).

(2)

Make BC vertical line pass through a, and the vertical foot is e.

AD is the center line of triangle ABC before folding,

Because ABC is a regular triangle, AD is perpendicular to BD and AD is perpendicular to CD.

Therefore, after folding in half,

And BD=DC=3/2.

It is easy to know that BDC is also a regular triangle, so BC=3/2.

Consider the folded triangle ABC.

AB=AC=3

AE is perpendicular to BC, so BE=EC, that is, BE=BC/2=3/4.

Consider the triangle Abel

One AE = √ (AB 2-BE 2) = (3 √15)/4

The answer given in the question is that the root number 15 is wrong.