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In a class of 33 students, 20 play cricket, 25 play football and 18 play volleyball. 15 play both cricket and football, 12 play both football and volleyball and 10 play both cricket and volleyball. If each student plays at least one game, find the number of students who play only cricket.
  • a)
    2
  • b)
    3
  • c)
    4
  • d)
    5
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In a class of 33 students, 20 play cricket, 25 play football and 18 pl...
Total = 33 = 20 + 25 + 18 - 15 - 12 - 10 + n(All three) + 0
n (All three) = 7

Now think of the cricket circle. 20 play cricket. 15 play cricket and football (including 7 who play all three). 10 play cricket and hockey (including 7 who play all three).
So 15 + 10 - 7 (because 7 is double counted, we subtract it once) = 18 play at least one sport other than cricket too.
Therefore, only 20 - 18 = 2 play cricket only.
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Community Answer
In a class of 33 students, 20 play cricket, 25 play football and 18 pl...

Let C, F and V denote the sets of number of students who play cricket, football and volleyball, respectively.
n(C) = 20, n(F) = 25 and n(V) = 18
n(C ∩ F) = 15, n(F ∩ V) = 12, n(C ∩ V) = 10
Let 'x' be the number of students who play all the 3 games.
Number of students who play both cricket and football, but not volleyball = (15 - x)
Similarly, number of students who play both football and volleyball, but not cricket = (12 - x)
Number of students who play both cricket and volleyball, but not football = (10 - x)
Now, we can find the number of students who play cricket only, football only and volleyball only as follows:
n(C) only = 20 - (15 - x + x + 10 - x) = x - 5
n(V) only = 18 - (10 - x + x + 12 - x) = x - 4
And n(F) only = 25 - (15 - x + x + 12 - x) = x - 2
33 = (x - 5) + (15 - x) + x + (10 - x) + (12 - x) + (x - 4) + (x - 2)
33 = x + 26
x = 7
Number of students who play only cricket = 7 - 5 = 2
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