Mathematical Notes

Research Article

A Problem in Combinations

A. C. Aitken

1. If there are n individuals A1, A2,.…, An, in how many ways can they be put into groups? For example, if there are three individuals A, B, C, they may be grouped as

S1757748900002334_eqn1

that is, in 5 ways, the respective subgroups, 1, 3, 1 in number, corresponding to the partitions 1 + 1 + 1, 1 + 2, 3 of the integer 3. Hence P (3), say, is 5.