Combinatorial number system 601 and 1010001011 = 651, which again shows that "C" comes before "C"<nowiki>'</nowiki>. This number is not however the one one wants to represent the "k"-combination with, since many binary numbers have a number of raised bits different from "k"; one wants to find the relative position of "C" in the ordered list of (only) "k"-combinations. The number associated in the combinatorial number system of degree "k" to a "k"-combination "C" is the number of "k"-combinations strictly less than "C" in the given ordering. This number can be computed from "C" = { "c", ..., "c", "c" } with "c"
Combinatorial number system of a set "S" is a subset of "S" with "k" (distinct) elements. The main purpose of the combinatorial number system is to provide a representation, each by a single number, of all formula_1 possible "k"-combinations of a set "S" of "n" elements. Choosing, for any "n", } as such a set, it can be arranged that the representation of a given "k"-combination "C" is independent of the value of "n" (although "n" must of course be sufficiently large); in other words considering "C" as a subset of a larger set by increasing "n" will not change the number that