Check sibling questions

Example 25 - In a class of 35 students, 24 like cricket, 16 football

Example 25 - Chapter 1 Class 11 Sets - Part 2


Transcript

Example 25 In a class of 35 students, 24 like to play cricket and 16 like to play football. Also, each student likes to play at least one of the two games. How many students like to play both cricket and football ? Let C be the set of students who like to play cricket & F be the set of students who like to play football. Number of students who like to play cricket = n(C) = 24 Number of students who like to play football = n(F) = 16 Number of students who like to play atleast cricket and football = n(C ∪ F) = 35 Number of students who like to play both cricket and football = n(C ∩ F) = ? We know that n ( C ∪ F ) = n ( C ) + n ( F ) – n ( C ∩ F ) 35 = 24 + 16 – n (C ∩ F) 35 = 40 – n (C ∩ F) n (C ∩ F) = 40 – 35 n (C ∩ F) = 5 Thus, 5 students like to play both games.

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.