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

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


 * $\left\{ {1, 2, 3 \mid 4}\right\}$
 * $\left\{ {1, 2, 4 \mid 3}\right\}$
 * $\left\{ {1, 3, 4 \mid 2}\right\}$
 * $\left\{ {2, 3, 4 \mid 1}\right\}$
 * $\left\{ {1, 2 \mid 3, 4}\right\}$
 * $\left\{ {1, 3 \mid 2, 4}\right\}$
 * $\left\{ {1, 3 \mid 2, 3}\right\}$