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?

Question

Smart Achievers · Accepted Answer

(5)

Let $X$ be the set of students who like to play cricket and $Y$ be the set of students who like to play football. Then, $X \cup Y$ is the set of students who like to play at least one game, and $X \cap Y$ is the set of students who like to play both games.

Given, $n (X) = 24,$ $n (Y) = 16,$ $n (X \cup Y) = 35$

Using $n (X \cup Y) = n (X) + n (Y) - n (X \cap Y),$

we get $35 = 24 + 16 - n (X \cap Y)$

Thus, $n (X \cap Y) = 5$

Solution

Q.
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

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Solution

Q. 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

Want Us to Email you About Special Offers & Updates?

Q.
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