determine the 5-combination at position 72. The successive values of for n = 4, 5, 6, ... are 0, 1, 6, 21, 56, 126, 252, ..., of which the largest one not exceeding 72 is 56, for n = 8. Therefore c5 = 8, and the remaining elements form the at position . The successive values of for n = 3, 4, 5, ... are 0, 1, 5, 15, 35, ..., of which the largest one not exceeding 16 is 15, for n = 6, so c4 = 6. Continuing similarly to search for a 3-combination at position one finds c3 = 3, which uses up the final unit; this establishes , and the remaining values ci will be the maximal ones with , namely . Thus we have found the 5-combination }. National Lottery example For each of the lottery combinations c1 < c2 < c3 < c4 < c5 < c6 , there is a list number N between 0 and which can be found by adding See also Factorial number system (also called factoradics) Primorial number system Asymmetric numeral systems - also e.g. of combination to natural number, widely used in data compression References Combinatorics Factorial and binomial topics