Let U be a set with 300 elements. (a) Suppose that we choose three subsets of U such that each of them contains 120 elements, the intersection of any two of them contains 37 elements, and the intersection between all three of them contains 9 elements. How many of the elements of U are in none of the three chosen subsets? (b) How many subsets of cardinality 3 are there in the set U? Justify your answers!

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