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)=32

n(C)=20

n(B)=18

n(F)=25

n(C∩B)=9

n(F∩B)=13

n(C∩F∩B)=5

Using formula,

n(U)=n(C)+n(B)+n(F)−n(C∩B)−n(F∩B)−n(C∩F)+n(C∩F∩B)

or,32=20+18+25−9−13−n(C∩F)+5

or,32=46−n(C∩F)

∴n(C∩F)=14

So, 14 students play both cricket and football.

Now,

no(C∩F)=n(C∩F)−n(C∩F∩B)

=14−5

Hence, 9 students liked to play football and cricket but not basketball.

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You might want to retry asking the question. It is unclear, and seems incomplete.

However, when you're dealing with 3 sets, the following formulae might come in handy.

n (A U B U C) = n(A) + n(B) + n(C) - n(A B) - n(A C) - n(B C) + n(A B C)

n(U) = n (A U B U C) + n (A U B U C)^c

where, A, B and C are three non-empty sets,
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