The principle of inclusion and exclusion of 3 sets says the following:
The Venn Diagram below shows the type of instruments that people like.
Find the following:
A,B,A,B,A,B, and CCC
contain the same number of element. Find a,b,a,b,a,b, and ccc
- 70 people like soccer.
- 60 people like basketball.
- 50 people like tennis.
- 25 people like soccer and basketball, but not tennis
- 10 people like soccer and tennis, but not basketball.
- 7 people like basketball and tennis, but not soccer
- 10 people like all three sports
How many people don't like any of the sports?
Willy surveyed 76 people for a cake shop. Each person ate at least one of the cakes: strawberry, chocolate and vanilla. Here is the information Willy got:
- 57 ate strawberry, 50 ate chocolate, and 39 ate vanilla.
- 20 ate both strawberry and chocolate, but not vanilla.
- 15 ate strawberry and vanilla, but not chocolate.
- 5 ate chocolate and vanilla, but not strawberry.
Who ate all three types of cakes?
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