Question

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​

Answer 1

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15 students do not play any of three games.

n(H ∪ B ∪ C) = 60 – 15 = 45

n(H ∪ B ∪ C) = n(H) + n(B) + n(C) – n(H ∩ B) – n(B ∩ C) – n(C ∩ H) + n(H ∩ B ∩ C)

45 = 23 + 15 + 20 – 7 – 5 – 4 + d

45 = 42 + d

d = 45- 42 = 3

Number of students who play all the three games = 3

Therefore, the number of students who play hockey, basketball and cricket = 3

a + d = 7

a = 7 – 3 = 4

b + d = 4

b = 4 – 3 = 1

a + b + d + e = 23

4 + 1 + 3 + e = 23

e = 15

Similarly, c = 2, g =14, f = 6

Number of students who play hockey but not cricket = a + e

= 4 + 15

= 19

Number of students who play hockey and cricket but not basketball = b = 1

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Hope It's Helpful.....:)