A cafeteria has 5 turkey sandwiches, 6 cheese sandwiches, and 4 tuna sandwiches. There are two students in line and each will take a sandwich. What is the probability that the first student takes a cheese sandwich and the next student takes a turkey sandwich?

(6/15)(5/14) = ?

To find the probability of the first student taking a cheese sandwich and the next student taking a turkey sandwich, we need to determine the total number of possible outcomes and the number of favorable outcomes.

First, let's determine the total number of possible outcomes. Each student can take any sandwich from the 15 sandwiches available. So, the total number of possible outcomes is 15 * 15 = 225.

Next, let's determine the number of favorable outcomes. The first student can choose from the 6 cheese sandwiches, and the second student can choose from the remaining 5 turkey sandwiches. So, the number of favorable outcomes is 6 * 5 = 30.

Therefore, the probability that the first student takes a cheese sandwich and the next student takes a turkey sandwich is 30/225, which simplifies to 2/15 or approximately 0.1333.