Sets

Rita Lamichhane

Student

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A survey was conducted among 300 students . It was found that 125 students like to play cricket . 145 students like to play football . 90 students like to play tennis . 32 students like to play exactly two games out of the three games. How many students like to play exactly one games?

  • 23 Dec, 2023
Replies (4)
Harit Thakuri

Instructor

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n(C) = 125, n(F) = 145, n(T) = 90
n(C ⋃ F ⋃ T) = 125 + 145 + 90 – [n(C ⋂ F) + n(F ⋂ T) + n(T ⋂ C)] + n(c ⋂ F ⋂ T)
300 = 360 – [n(C ⋂ F) + n(F ⋂ T) + n(T ⋂ C)] + n(c ⋂ F ⋂ T)
n(C ⋂ F) + n(F ⋂ T) + n(T ⋂ C) = 60 + n(c ⋂ F ⋂ T)….(i)
Also, given that,
n(C ⋂ F) + n(F ⋂ T) + n(T ⋂ C) – 3[n(c ⋂ F ⋂ T)] = 32
n(C ⋂ F) + n(F ⋂ T) + n(T ⋂ C) = 32 + 3[n(c ⋂ F ⋂ T)]….(ii)
From (i) and (ii),
60 + n(c ⋂ F ⋂ T) = 32 + 3[n(c ⋂ F ⋂ T)]
60 – 32 = 3[n(c ⋂ F ⋂ T)] – n(c ⋂ F ⋂ T)
2[n(c ⋂ F ⋂ T)] = 28
n(c ⋂ F ⋂ T) = 14
Number of students like to play exactly one game = n(C) + n(F) + n(T) – 2[n(C ⋂ F) + n(F ⋂ T) + n(T ⋂ C)] + 3[n(c ⋂ F ⋂ T)]
= 125 + 145 + 90 – 2[32 + 3 × 14] + 3 × 14
= 360 – 148 + 42
= 254


:)Happy Learning

  • 23 Dec, 2023

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