Math Problem Statement

  1. In a class of 60 students, 23 play hockey, 15 play basketball,20 play cricket and 7 play hockey and basketball, 5 play cricket and basketball, 4 play hockey and cricket, 15 do not play any of the three games. Find (i) How many play hockey, basketball and cricket (ii) How many play hockey but not cricket (iii) How many play hockey and cricket but not basketball

Solution

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Math Problem Analysis

Mathematical Concepts

Set Theory
Venn Diagrams
Inclusion-Exclusion Principle

Formulas

|H ∪ B ∪ C| = |H| + |B| + |C| - |H ∩ B| - |B ∩ C| - |H ∩ C| + |H ∩ B ∩ C|
|H \setminus C| = |H| - |H ∩ C|

Theorems

Inclusion-Exclusion Principle

Suitable Grade Level

Grades 9-12

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