Please answer the following questions in the attached image (Course: discrete structures and combination analysis) :

1. (2 marks) Let S={0,1,2,3,4,5,6,7,8,9,10}. How many subsets with five elements contain at least one of the following elements: 2,4,6,8. Explain your reasoning. Strings contaaning all elements 115 Stringe coftaining 2,4,6,8=11510510515105 = Ans 44+7=256+7=263 (2 marks) How many people are needed to guarantee that at least two were born on the same day of the week and in the same month (perhaps in different years)? Explain your answer. Days in weak =7, Monthe =12 =712=84PPl To guarantel atteast 2 on the same day we reed +1 pogll to be borne 85 prle