A Problem in Combinations

1. If there are n individuals A 1 , A 2 ,.…, A n , 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 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.