Number of Set Partitions by Number of Components/Examples/4 into 2

Example of Number of Set Partitions
A set with $4$ elements $\set {1, 2, 3, 4}$ can be partitioned into $2$ subsets in $\displaystyle \set {4 \atop 2} = 7$ ways:


 * $\set {1, 2, 3 \mid 4}$
 * $\set {1, 2, 4 \mid 3}$
 * $\set {1, 3, 4 \mid 2}$
 * $\set {2, 3, 4 \mid 1}$
 * $\set {1, 2 \mid 3, 4}$
 * $\set {1, 3 \mid 2, 4}$
 * $\set {1, 3 \mid 2, 3}$