Remember that the important aspect of this assignment is not the
answer, but the solution.We areÂ not looking for an
explanation which includes all of your reasoning, but just a
simple, clear, thoughtful, direct, short explanation. Donâ€™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 â€˜set,â€™ â€˜spaces,â€™ â€˜listâ€™ or â€˜chooseâ€™ 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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