English: Two ways of constructing a family of subsets of r items out of n, such that all subsets intersect each other and there are as many subsets as possible (matching the bound of the Erdős–Ko–Rado theorem): left, a family formed by fixing one item x and choosing the other r − 1 items in all possible ways; right (for n = 2r), a family formed by avoiding one item x and choosing r of the remaining items in all possible ways. In this example, n = 4 and r = 2; the largest possible intersecting families of subsets have three sets.