(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?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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