Final answer:
In this problem, we calculate the number of divisions possible when 8 new teachers are divided among 4 schools. We also calculate the number of divisions when each school must receive 2 teachers.
Step-by-step explanation:
In this problem, we are dividing 8 new teachers among 4 schools. Each teacher can be assigned to any of the 4 schools, so for each teacher, there are 4 possible divisions. Since there are 8 teachers in total, we can find the total number of divisions by multiplying the number of possibilities for each teacher together: 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 = 4^8 = 65,536.
If each school must receive 2 teachers, we can consider it as distributing 8 teachers into groups of 2. The number of divisions can be determined by the combination formula, which can be written as C(n, r) = n! / (r! * (n-r)!), where n is the total number of items and r is the number of items in each group.
Using the combination formula, we can calculate the number of divisions as C(8, 2) = 8! / (2! * (8-2)!) = 8! / (2! * 6!) = (8 * 7) / (2 * 1) = 28.