Answer:
To find the number of students who play both hockey and football, you can use the principle of the inclusion-exclusion principle.
Let's denote:
- H as the number of students who play hockey.
- F as the number of students who play football.
- N as the number of students who play neither game.
According to the information provided:
- H = 25 (students who play hockey)
- F = 30 (students who play football)
- N = 8 (students who play neither game)
- The total number of students = 50
We want to find the number of students who play both hockey and football, denoted as H ∩ F.
Now, we can use the inclusion-exclusion principle formula:
Total = H + F - (H ∩ F) + N
Plugging in the values:
50 = 25 + 30 - (H ∩ F) + 8
Now, solve for H ∩ F:
(H ∩ F) = 25 + 30 + 8 - 50
(H ∩ F) = 63 - 50
(H ∩ F) = 13
So, there are 13 students who play both hockey and football.