In a group of 50 students, 25 play Hockey, 30 play Football, and 8 play neither game. What is the number of students who play both Hockey and Football?

Options

A. (a) 10
B. (b) 11
C. (c) 12
D. (d) 13

Explanation

To find the number of students who play both Hockey and Football, we can follow these steps:

### Step 1: Identify the total number of students and those who play neither game.
- Total number of students = 50
- Number of students who play neither game = 8

### Step 2: Calculate the number of students who play at least one game.
- Students who play at least one game = Total students - Students who play neither
- Students who play at least one game = 50 - 8 = 42

### Step 3: Identify the number of students who play Hockey and Football.
- Number of students who play Hockey = 25
- Number of students who play Football = 30

### Step 4: Use the principle of inclusion-exclusion to find the number of students who play both games.
The formula for the number of students who play at least one game is:
\[ \text{Number of Hockey players} + \text{Number of Football players} - \text{Number of students who play both games} = \text{Students who play at least one game} \]
Let \( x \) be the number of students who play both games. Then we can set up the equation:
\[ 25 + 30 - x = 42 \]

### Step 5: Solve for \( x \).
- Combine the numbers:
\[ 55 - x = 42 \]
- Rearranging gives:
\[ x = 55 - 42 \]
- Therefore:
\[ x = 13 \]

### Conclusion:
The number of students who play both Hockey and Football is **13**.

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