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Remember that the important aspect of this assignment is not the answer, but the solution.We are  not looking for an explanation which includes all of your reasoning, but just a simple, clear, thoughtful, direct, short explanation. Don’t try to explain you arithmetic, just how we use what we know (mostly addition and multiplication principle) to determine the answer.
It is important that if you make a connection between the problem and the answer so we am going to impose two important rules: (a) you must start your solution with the question (RECOPY IT!) (b) if you use words like ‘set,’ ‘spaces,’ ‘list’ or ‘choose’ it needs to be clear how these things are related to non-negative integers for the rst problem and sequences of cards for the second.
(1) How many solutions to the equation x1 + x2 + x3 + x4 + x5 + x6 = 20 are there where each of the xi are non-negative integers and x1 + x2 is divisible by 6? Answer: 8,866 (2) How many ordered sequences of 4 cards are there with (at least) two consecutive cards that are the same rank? Answer: 1,093,560



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