In a class of 30 students, 18 students play soccer, 15 students play basketball and 5 students play both sports. Determine the number of students who play either soccer or basketball or both

To solve the problem, we'll use the principle of inclusion-exclusion.

### Step 1: Define the sets
- Let \( S \) be the set of students who play soccer.
- Let \( B \) be the set of students who play basketball.

### Step 2: Given values
- \( |S| = 18 \) (students who play soccer)
- \( |B| = 15 \) (students who play basketball)
- \( |S \cap B| = 5 \) (students who play both soccer and basketball)

### Step 3: Apply the principle of inclusion-exclusion
The number of students who play either soccer, basketball, or both is given by the formula:

\[
|S \cup B| = |S| + |B| - |S \cap B|
\]

### Step 4: Substitute the given values into the formula
\[
|S \cup B| = 18 + 15 - 5 = 28
\]

### Conclusion:
There are 28 students who play either soccer or basketball or both.

Would you like further details or have any questions?

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Here are 5 related questions:
1. How many students play only soccer?
2. How many students play only basketball?
3. How many students do not play either soccer or basketball?
4. If 7 additional students start playing soccer, how would that affect the total?
5. What is the probability that a randomly chosen student plays both sports?

**Tip:** When working with sets and overlapping groups, always consider the principle of inclusion-exclusion to avoid double-counting.

In a class of 30 students, 18 students play soccer, 15 students play basketball and 5 students play both sports. Determine the number of students who play either soccer or basketball or both.

Determine how many students in a class play either soccer, basketball, or both using the principle of inclusion-exclusion. This problem explores key concepts in set theory, perfect for students in Grades 6-8.

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