Yes, counting is hard. We may as well get that out and understood right at the top. “Counting” is short for “enumerative combinatorics,” which certainly doesn’t sound easy. This is a course in discrete mathematics that addresses questions that begin, How many ways are there to ... . For example, we shall soon know the answer to questions such as, How many ways are there to order 12 ice cream cones if 8 flavors are available? At the end of the course we should be able to answer such nontrivial counting questions as, How many ways are there to color the faces of a cube if k colors are available, with each face having exactly 1 color? or How many ways are there to stack n poker chips, each of which can be red, white, blue, or green, such that each red chip is adjacent to at least 1 green chip?
KeywordsInteger Solution Elementary Enumeration Round Table Distinguishable Object Positive Integer Solution
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