3. Jackmerius is taking 8 courses this year. How many ways can he select his block A, B, C, D, classes for first semester?

## Step 1: Understanding the Problem<br />### Jackmerius needs to choose 4 courses out of 8 for his first semester. The order in which he chooses the courses matters, as different orderings represent different block schedules (A, B, C, D). This is a permutation problem.<br /><br />## Step 2: Applying the Permutation Formula<br />### We can use the permutation formula to solve this. The formula for permutations is given by $_nP_r = \frac{n!}{(n-r)!}$, where $n$ is the total number of items and $r$ is the number of items being chosen. In this case, $n = 8$ (total courses) and $r = 4$ (courses chosen for the first semester). So, we need to calculate $_8P_4$.<br />$_8P_4 = \frac{8!}{(8-4)!} = \frac{8!}{4!} = \frac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{4 \times 3 \times 2 \times 1} = 8 \times 7 \times 6 \times 5 = 1680$