Method of distinguished element

Definition

Examples

• The binomial coefficient is the number of size-k subsets of a size-n set. A basic identity—one of whose consequences is that the binomial coefficients are precisely the numbers appearing in Pascal's triangle—states that:
• The number of subsets of any size-n set is 2ⁿ.
• Let B_n be the nth Bell number, i.e., the number of partitions of a set of n members. Let C_n be the total number of "parts" among all partitions of that set. For example, the partitions of the size-3 set may be written thus: