The Fundamental Counting Principle is introduced with the question, "What are the chances of rolling two ones and a two with three dice?" The total number of outcomes is shown and counted. This leads to the development of the general formula of the total number of possible arrangements. Finally, the program defines a permutation as an ordered arrangement of things drawn from a given number. (10 minutes)

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Part of the Series : Combinatorics


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		Permutations In this show, permutations are examined in terms of simple illustrative examples. We see an elegant method of expressing the permutation formula using factorial notation. Finally, a general formula is derived for arranging n objects when some of the ...(more details)
		Combinations In this program, combinations are defined and a general notation and formula are derived. Combinatorial concepts are used to solve some ordinary playing-card problems such as determining the number of five-card poker hands that can be dealt from a fu...(more details)
		Binomial Theorem This program begins with Pascal's triangle, the mathematical sequences hidden within it (such as the Fibonacci), and how this relates to the real world. The show draws connections between Pascal's triangle, combinations, binomial expansions, and the ...(more details)
		Problem Solving This program applies what the student has learned about combinations and permutations to the real world. The famous Birthday Problem and Envelope Stuffing puzzles are examined to derive mathematical sequences that lead us inevitably to Euler's consta...(more details)
		A Dicey Beginning This program introduces the science of combinatorics in a historical perspective. The question of determining the settlement of an interrupted game of dice intrigued Blaise Pascal and Pierre Fermat, and their efforts to resolve the problem eventually...(more details)

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