Q: In how many ways can 4 labeled balls go into 2 identical nonempty boxes? S(4,2): partitions of {1,2,3,4} into 2 subsets. One triple + one single: C(4,1) = 4 ways. Two pairs: {12|34}, {13|24}, {14|23} = 3 ways. Total: 4+3 = 7 = S(4,2)!