a) In a canteen, every day a chef prepares three lunch options customers can choose from. He is not a very good chef, but he knows six meals he can prepare very well. Every day, he chooses three out of these six and offers them. The options are presented left to right and we consider a lunch different if the three options are in different order, even if they are the same. For how many days can the chef go on, without repeating himself?
b) The customers have seen through chef’s plot and they realized that the order of the options does not in fact matter – there are still the same three lunches to choose from. If the chef now wants every day to be different, for how many days can he prepare different three meals each day?