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Q29 (CISF/2026) Miscellaneous & General Knowledge › Important Days, Places & Events

In a class of 50 students, 20 students play cricket, 15 students play football and 10 students play both cricket and football. How many students play neither cricket nor football ?

Result
Your answer: —  Â·  Correct: D

Explanation

This problem can be solved using the principle of set theory and Venn diagrams. Let C be the set of students who play cricket and F be the set of students who play football.

  • Total number of students (Universal set, n(U)) = 50
  • Students playing cricket, n(C) = 20
  • Students playing football, n(F) = 15
  • Students playing both, n(C ∩ F) = 10

First, calculate the number of students who play at least one of the two games using the formula: n(C ∪ F) = n(C) + n(F) - n(C ∩ F).

n(C ∪ F) = 20 + 15 - 10 = 25.

The number of students who play neither cricket nor football is the total number of students minus those who play at least one game: 50 - 25 = 25.

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SIMILAR QUESTIONS

CAPF · 2024 · Q28 Relevance score: 7.08

Out of a class of 100 students, 25 play at least cricket and football, 15 play at least cricket and hockey, 12 play at least football and hockey and 10 play all the three sports. The number of students playing cricket, football and hockey are 50, 37 and 22, respectively. The number of students who do NOT play any of the three sports is

CAPF · 2020 · Q124 Relevance score: 5.75

In a group of 100 children, 64 children like to play cricket, 53 children like to play football and 20 children like to play both cricket and football. How many children do NOT like to play cricket or football ?

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IAS · 1998 · Q143 Relevance score: 0.55

There are 50 students admitted to a nursery class. Some students can speak only English and some can speak only Hindi. 10 students can speak both English and Hindi. If the number of students who can speak English is 21, then how many students can speak Hindi, how many can speak only Hindi and how many can speak only English ?

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A schoolteacher has to select the maximum possible number of different groups of 3 students out of a total of 6 students. In how many groups any particular student will be included?