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""k", ..., "c"2, "c"1 } with "c""k" > ... > "c"2 > "c"1 as follows. From the definition of the ordering it follows that for each "k"-combination "S" strictly less than "C", there is a unique index "i" such that "c""i" is absent from "S", while "c""k", ..., "c""i"+1 are present in "S", and no other value larger than "c""i" is. One can therefore group those "k"-combinations "S" according to the possible values 1, 2, ..., "k" of "i", and count each group separately. For a given value of "i" one must include