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When we count functions, we consider the following two functions, for example, to be different:

\begin{equation*} f = \twoline{1 \amp 2 \amp 3 \amp 4\amp 5 \amp 6 \amp 7}{a \amp b \amp c \amp c \amp c \amp c \amp c} \qquad g = \twoline{1 \amp 2 \amp 3 \amp 4\amp 5 \amp 6 \amp 7}{b \amp a \amp c \amp c \amp c \amp c \amp c}\text{.} \end{equation*}

But these two functions would correspond to the same cookie distribution: kids \(a\) and \(b\) each get one cookie, kid \(c\) gets the rest (and none for kid \(d\)).

in-context