Sets, Relations & Functions
Inclusion-Exclusion — Medals in Sports
nta_pyq_2023_apr
Grade 11
Question:
In 60 athletes who won medals, $n(A)=48$, $n(B)=25$, $n(C)=18$, $n(A\cap B\cap C)=5$. Number winning exactly two events is
Step-by-Step Solution
Key Concept: $n(A\cup B\cup C)=n(A)+n(B)+n(C)-n(A\cap B)-n(A\cap C)-n(B\cap C)+n(A\cap B\cap C)$. Exactly two: sum of pairwise intersections $-3n(A\cap B\cap C)$.
21 athletes.
Correct Answer: 2