In a school 200 student play football ,150 play cricket and 70 played both.how many play?
A=only football
B=only cricket
To find the number of students who play only football (A) and only cricket (B), we can use the principle of inclusion-exclusion.
Given:
Number of students who play football (F) = 200
Number of students who play cricket (C) = 150
Number of students who play both football and cricket (F ∩ C) = 70
To find A (students who play only football), we need to subtract the students who play both football and cricket (F ∩ C) from the total number of students who play football (F). Similarly, to find B (students who play only cricket), we subtract the students who play both football and cricket (F ∩ C) from the total number of students who play cricket (C).
A = F - (F ∩ C)
B = C - (F ∩ C)
Substituting the given values:
A = 200 - 70 = 130
B = 150 - 70 = 80
Therefore, there are 130 students who play only football (A) and 80 students who play only cricket (B).