Currently i have (i!12-i!)/12! but not sure if it is the correct way to approach it

Suppose six dogs and six cats run in a race. Assume that each of the 12! rankings of the animals are equally likely. Let X denote the highest ranking achieved by a dog; e.g., X = 1 if the top-ranked animal is a dog. Compute P(X = i) for i = 1, 2, . .., 12