Finite Sets and Cardinality Sets containing a finite number of elements are called finite sets For a finite set E the number of its elements is called the cardinality of E . Let A , B E . Counting Problems I.2.a. For each of these he has the choice of two vests and, finally, three pairs of shoes for each the resulting 48 different dresses. The mathematical reformulation of the above principle is nothing but the identity for the cardinality of Cartesian products.
E r is the set of all possible outcomes of the sequence of the r experiments.
The number of mappings from a set having k elements to a set having n elements equals n k . Contrary to the problem discussed above the members of the committee are not distinguishable by different tasks. A committe of k has to be formed from agroup of n persons. Mimicking the above argument we find that there are possible 5-card poker hands. Unordered selections are called combinations .