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The problem of enumerating ''k''-tuples whose sum is ''n'' is equivalent to the problem of counting configurations of the following kind: let there be ''n'' objects to be placed into ''k'' bins, so that all bins contain at least one object. The bins are distinguished (say they are numbered 1 to ''k'') but the ''n'' objects are not (so configurations are only distinguished by the ''number of objects'' present in each bin). A configuration is thus represented by a ''k''-tuple of positive integers.
The ''n'' objects are now represented as a row of ''n'' stars; adjacent bins are separated by bars. The configuration will be specified by indicating the boundary between the first and second bin, the boundary between the second and third bin, and so on. Hence {{math|''k'' − 1}} bars need to be placed between stars. Because no bin is allowed to be empty, there is at most one bar between any pair of stars. There are {{math|''n'' − 1}} gaps between stars and hence {{math|''n'' − 1}} positions in which a bar may be placed. A configuration is obtained by choosing {{math|''
===Example===
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