answer all questions with explanation

4. (10 marks total) Ancient Romans enjoyed games of dice. The game T esseme uses three sixsided dice, i.e. cubes, the faces numbered from one to six. The three dice are thrown at the same time, and the numbers are read off of each dice and added up. The best score is the highest sum: three sixes. (a) (1 mark) What is the probability of throwing three sixes? (b) (5 marks) Write down a generating function of the sequence 3,, where 87, is the number of ways for the sum of the three numbers thrown to be 7;. (c) (4 marks) Use a computer package (Mathematica, WolframAlpha, Sagemath, ...) to com pute which sum has the highest probability, and what this probability is. (Submit the text of the code you used, and what kind of package you used for the computation, as well as the numerical result.)