Of Thee I Sing (opens in new tab)

A set of 4 elements can be partitioned in 15 ways. Pleasingly, this is also the number of rhyme schemes that a 4-line poem can take: AAAA, AAAB, AABA, AABB, AABC, ABAA, ABAB, ABAC, ABBA, ABBB, ABBC, ABCA, ABCB, ABCC, ABCD. A poem with 5 lines has 52 possible schemes, corresponding to the partitions of a 5-element set, and so on. These are called Bell numbers.