8. A classroom has desks arranged in 6 rows and 7 columns, with 40 students. Two positions in the last row are left empty, and the rest of the students are seated based on their height and vision. There are 24 students who are tall, 18 students who have good vision, and 6 students who have both conditions. It is known that if a student is short and has poor vision, they must sit in the first three rows; if a student is tall and has good vision, they must sit in the last three rows. Let the method of seating arrangement be $A$, then the number of times 2 appears in the prime factorization of $A$ is $\qquad$
8. 35 .

The number of students who are short and have poor eyesight is 4, the number of students who are tall and have good eyesight is 6, and the remaining students number 30 people.

The number of ways to leave two seats empty in the last row is $C_{7}^{2}$, where the power of 2 is 0;

The number of ways to arrange the students who are short and have poor eyesight is $A_{21}^{4}$, where the power of 2 is 3;

The number of ways to arrange the students who are tall and have good eyesight is $A_{19}^{6}$, where the power of 2 is 6;

The number of ways to arrange the other students is $\mathrm{A}_{30}^{30}$, where the power of 2 is $15+7+3+1=26$.
Therefore, the total power of 2 is 35.