Question

In a group of 50 students, 25 play hockey, 30 play football and 8 play neither game. Find the number of students who play both games?

Answer 1

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.