In a group of students , 65 play football , 42 play hockey , 20 play football and hockey , 25 play football and cricket , 25 play hockey and cricket and 8 play all three game.
Let F . H . And C represent the set of students who play football , hockey and cricket respectively.
sketeh venn diagram represent above data.
Then find :
1] Number of students who play football only .
2]Number of students who play hockey
only .
3]Number of students who play cricket only .
4]Number of students who play both football and hockey only .
5]Number of students who play both hockey and cricket only .
6]Number of students who play both football and cricket.
To solve this problem, let's create a Venn diagram to represent the given data.
Step 1: Draw three overlapping circles representing football (F), hockey (H), and cricket (C).
Step 2: Label the overlapping regions based on the given information.
- The region where all three circles overlap represents the students who play all three games. In this case, it is given that 8 students play all three games, so label this region as 8.
- The regions where only two circles overlap represent the students who play both of those games but not the third. It is given that 20 students play football and hockey, 25 students play football and cricket, and 25 students play hockey and cricket.
- The regions where only one circle is present represent the students who play only that game.
Now that we have drawn the Venn diagram, we can answer the questions:
1] Number of students who play football only: The region labeled only as F represents the students who play football only. Count the number of students in this region.
2] Number of students who play hockey only: The region labeled only as H represents the students who play hockey only. Count the number of students in this region.
3] Number of students who play cricket only: The region labeled only as C represents the students who play cricket only. Count the number of students in this region.
4] Number of students who play both football and hockey only: The region where only F and H overlap represents the students who play both football and hockey but not cricket. Count the number of students in this region.
5] Number of students who play both hockey and cricket only: The region where only H and C overlap represents the students who play both hockey and cricket but not football. Count the number of students in this region.
6] Number of students who play both football and cricket: The region where only F and C overlap represents the students who play both football and cricket but not hockey. Count the number of students in this region.
By counting the number of students in the relevant regions, we can find the answers to all these questions.