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Question

# In a group of students, 65 play football, 45 play hockey, 42 play cricket, 20 play football and hockey, 25 play football and cricket, 15 play hockey and cricket, and 8 play all three games. Find the total number of students in the group. (Assume that each student in the group plays at least one game.)

A
100
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B
35
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C
57
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D
125
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Solution

## The correct option is A: 100Let F, H and C represent the set of students who play football, hockey and cricket respectively.From the given information, we have n(F)=65, n(H)=45, n(C)=42, n(F∩H)=20, n(F∩C)=25, n(H∩C)=15 n(F∩H∩C)=8 From the above diagram,we have Total number of students in the group =28+12+18+7+10+17+8 =100 Hence, the total number of students in the group is 100.

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