A guy called Chevalier de M ´er ´e once asked the mathematician Blaise Pascal for help: He had noted that by throwing 3 dice, the sum of 11 appeared more often than the sum 12. He argued that this could not be true since 11 can be obtained by the combinations 6-4-1,6-3-2,5-5-1,5-4-2,5-3-3,4-4-3 and there are also 6 combinations which lead to the sum 12.
a) What are the combinations which lead to the sum 12?
b) Is the observation of the Chevalier de M ´er ´e just an exception due to randomness or is his argumentation wrong? Define a suitable sample space to solve this question.