On the planet Zog, the lottery has a different set of rules to the ones us mortals are accustomed to on Earth. Each alien can choose 8 distinct numbers from a choice of 60, and each week 12 numbers are drawn without replacement live on ZogTV to give an unordered set of winning numbers. Aliens who have chosen all of their 8 numbers correctly get a tier 1 prize, aliens who have chosen 7 numbers correctly get a tier 2 prize and so on, until aliens who have chosen only one number correctly receive a tier 8 prize. Let Pk be the probability of winning a tier k prize once you have chosen your numbers. Find a general formula for Pk in terms of k.