At least one game – count using inclusion-exclusion: In a class, 50 students play cricket, 20 play football, and 10 play both. How many students play at least one of these two games?

Introduction / Context:Counting those who play at least one of two sports requires inclusion-exclusion to avoid double-counting those who play both.

Given Data / Assumptions:

• |C| = 50 (cricket)
• |F| = 20 (football)
• |C ∩ F| = 10

Concept / Approach:|C ∪ F| = |C| + |F| − |C ∩ F|.

Step-by-Step Solution:|C ∪ F| = 50 + 20 − 10 = 60

Verification / Alternative check:At least one = only cricket (40) + only football (10) + both (10) = 60.

Why Other Options Are Wrong:45, 55, 65 do not respect the overlap structure.

Common Pitfalls:Adding 50 and 20 without subtracting the overlap.

Final Answer:60