In a school, 20 students play cricket, 30 play basketball and 50 play hockey. If the number of students who play exactly one game is 30 and the number of students who play exactly two games is 20, find the number of students who play all the three games.151016Cannot be determined
Question
In a school, 20 students play cricket, 30 play basketball and 50 play hockey. If the number of students who play exactly one game is 30 and the number of students who play exactly two games is 20, find the number of students who play all the three games.151016Cannot be determined
Solution
Let's solve this step by step:
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First, add up the total number of students who play each game: 20 (cricket) + 30 (basketball) + 50 (hockey) = 100 students.
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According to the problem, there are 30 students who play exactly one game and 20 students who play exactly two games.
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The students who play two games are counted twice in our initial total (once for each game they play). So, subtract twice the number of students who play two games from the total: 100 - 2*20 = 60.
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Similarly, the students who play one game are counted once in our initial total. So, subtract the number of students who play one game from the total: 60 - 30 = 30.
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The remaining students are those who play all three games. So, there are 30 students who play all three games.
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