(a) Suppose that we choose three subsets of M such that each of them con- tains 100 elements, the intersection of any two of them contains 32 ele- ments, and the intersection between all three of them contains 8 ele- ments. How many of the elements of M are in none of the three chosen subsets? (b) How many subsets of cardinality 3 are there in the set M?

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4. Let M be a set with 250 elements.
(a) Suppose that we choose three subsets of M such that each of them con-
tains 100 elements, the intersection of any two of them contains 32 ele-
ments, and the intersection between all three of them contains 8 ele-
ments. How many of the elements of M are in none of the three chosen
subsets?
(b) How many subsets of cardinality 3 are there in the set M?
Motivera dina svar!
Transcribed Image Text:4. Let M be a set with 250 elements. (a) Suppose that we choose three subsets of M such that each of them con- tains 100 elements, the intersection of any two of them contains 32 ele- ments, and the intersection between all three of them contains 8 ele- ments. How many of the elements of M are in none of the three chosen subsets? (b) How many subsets of cardinality 3 are there in the set M? Motivera dina svar!
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