At a local market judges ranked eight different homemade marmalades from best to worst according to various criteria. Amy purchases four different marmalades at random to take home. (a) (5 marks] What is the sample space? (b) (5 marks) How many possible ways can Amy choose four different marmalades from the eight available? (c) (10 marks) Find the probability that the best marmalade among those Amy purchased is actually ranked third by the judges among the original eight (d) (10 marks) Find the probability that the worst marmalade among those Amy purchased is actually ranked seventh by the judges among the original eight. (e) [15 marks) Find the probability that the best and worst marmalades among those Amy purchased are actually ranked third and seventh respectively by the judges among the original eight. Are these two events independent