Find the number of different ways that an instructor can choose 4 students from a class of 33 students for a field thp

Step 1 ：This is a combination problem. In a combination, order does not matter. We are choosing 4 students out of 33, so we need to calculate the number of combinations of 33 taken 4 at a time. The formula for combinations is \(C(n, k) = \frac{n!}{k!(n-k)!}\), where n is the total number of items, k is the number of items to choose, and ! denotes factorial.

Step 2 ：Let's substitute the given values into the formula. Here, n = 33 and k = 4.

Step 3 ：Calculate the factorial of n, k, and (n-k).

Step 4 ：Substitute these values into the formula to get the number of combinations.

Step 5 ：The number of different ways that an instructor can choose 4 students from a class of 33 students for a field trip is \(\boxed{40920}\).