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$\{1,2,3\}, \{4\}$
$\{1,2,4\}, \{3\}$
$\{1,3,4\}, \{2\}$
$\{2,3,4\}, \{1\}$
$\{1,2\}, \{3,4\}$
$\{1,3\}, \{2,4\}$
$\{1,4\}, \{2,3\}$
Total: $7$ partitions. Since the slots are indistinct, these are all valid and distinct only by labeling of the subsets.
So total number of configurations is:
S(4,1) + S(4,2) = 1 + 7 = 8