Ebon will be inviting 50 friends, and they will be reaching the island on Ebon's huge private yacht. The party will take place on the weekend, but the friends can travel on the yacht to the island either on the Tuesday, Wednesday, Thursday, or Friday before the weekend. Each friend will choose the travel day that is most convenient for them. a) What is the largest number of people that are guaranteed to arrive the same day? b) How many different distributions of people by arrival date are there? for example one distribution might be 12 people on Tuesday, 8 on Wednesday, 23 on Thursday, and 7 on Friday. Explain your answers. Time

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