A counting technique in combinatorics, so named because of the notation used. For example: how many triples (x,y,z) of non-negative integers are there such that x+y+z = 100? Each such triple can be represented as (⋆∙∙∙⋆|⋆∙∙∙⋆|⋆∙∙∙⋆) where there are 100 stars, separated by 2 bars into x, then y, then z stars. So there are $\left(\begin{array}{c}102\\ 2\end{array}\right)$ ways of choosing where to place the 2 bars, and so this number of triples. If we insist x,y,z are positive, then the answer is $\left(\begin{array}{c}99\\ 2\end{array}\right)$, as 3 of these choices have been made.