In a school, all students play either football or cricket or both. If 250 play football, 300 play cricket and 120 play both the games, then find the total number of students in the school.

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Solution

If the sets F and C stand for the sets of students that play football and cricket respectively, then by question

$n (F) = 250, n (C) = 300$ and $n (F \cap C) = 120.$

$But, n (F \cup C) = n (F) + n (C) - n (F \cap C) .$

$= 250 + 300 - 120$

$= 430$

Thus, the total number of students in the school is 430.

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In a school, all students play either football or cricket or both. If 250 play football, 300 play cricket and 120 play both the games, then find the total number of students in the school.

If the sets F and C stand for the sets of students that play football and cricket respectively, then by question n(F)=250, n(C)=300 and n(F∩C)=120. But, n(F∪C)=n(F)+n(C)−n(F∩C). =250+300–120 =430 Thus, the total number of students in the school is 430.