In a group of 80 students, 50 play football, 45 play cricket and each student plays either football or cricket. Find the number of students who play both the games.

Question

Smart Achievers · Accepted Answer

(3)

$Let F be the set of the students who play football$ $and C be the set of students who play cricket.$

$Then n (F) = 50 and n (C) = 45 .$

$Since each of the 80 students play atleast one of the two games,$

$we have n (F \cup C) = 80 .$

$n (F \cap C) = n (F) + n (C) - n (F \cup C) = 50 + 45 - 80 = 15 .$

Solution

Q.
In a group of 80 students, 50 play football, 45 play cricket and each student plays either football or cricket. Find the number of students who play both the games.

1 12

2 14

3 15

4 18

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