# §26.17 The Twelvefold Way

The twelvefold way gives the number of mappings $f$ from set $N$ of $n$ objects to set $K$ of $k$ objects (putting balls from set $N$ into boxes in set $K$). See Table 26.17.1. In this table $\left(k\right)_{n}$ is Pochhammer’s symbol, and $\mathop{S\/}\nolimits\!\left(n,k\right)$ and $\mathop{p_{k}\/}\nolimits\!\left(n\right)$ are defined in §§26.8(i) and 26.9(i).

Table 26.17.1 is reproduced (in modified form) from Stanley (1997, p. 33). See also Example 3 in §26.18.