Set Theory

Step 1: Define the sets and list the given information.
Let F be the set of students who registered for football. Let B be the set of students who registered for basketball. We are given: - Number of students in football, - Number of students in basketball, - Total number of students, which is the number of students in at least one of the games, .

Step 2: Use the Principle of Inclusion-Exclusion.
The formula for two sets is: We want to find the number of students registered in both games, which is .

Step 3: Substitute the given values and solve for . So, 25 students registered for both games.