37 Maths -- Set

Each student in a class of 32 plays at least one game: cricket, football, or basketball. 20 play cricket, 18 play basketball, and 25 play football. 9 play cricket and basketball, 13 play football and basketball and 5 play all three. Find the number of students who play:solution;Let U be...

Each student in a class of 32 plays at least one game: cricket, football, or basketball. 20 play cricket, 18 play basketball, and 25 play football. 9 play cricket and basketball, 13 play football and basketball and 5 play all three. Find the number of students who play:

solution;

Let U be the set of total students in the class.Let C,F and B represent the sets of students who play Cricket, Football and Basketball, respectively.Here,n(U)=32n(C)=20n(B)=18n(F)=25n(CB)=9n(FB)=13n(CFB)=5Using formula,n(U)=n(C)+n(B)+n(F)n(CB)n(FB)n(CF)+n(CFB)or,32=20+18+25913n(CF)+5or,32=46n(CF)n(CF)=14So, 14 students play both cricket and football.Now,no(CF)=n(CF)n(CFB)=145=9Hence, 9 students liked to play football and cricket but not basketball.

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