Essential Permutations & Combinations: A Self-Teaching Guide

Tim Hill

qer 2018 · Questing Vole Press

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The mathematics of counting permutations and combinations is required knowledge for probability, statistics, professional gambling, and many other fields. But counting is hard. Students find it hard. Teachers find it hard. And in the end the only way to learn is to do many problems. Tim Hill's learn-by-example approach presents counting concepts and problems of gradually increasing difficulty. If you become lost or confused, then you can back up a bit for clarification. With practice, you'll develop the ability to decompose complex problems and then assemble the partial solutions to arrive at the final answer. The result: learn in a few weeks what conventional schools stretch into months.

- Teaches general principles that can be applied to a wide variety of problems.

- Avoids the mindless and excessive routine computations that characterize conventional textbooks.

- Treats counting as a logically coherent discipline, not as a disjointed collection of techniques.

- Restores proofs to their proper place to remove doubt, convey insight, and encourage precise logical thinking.

- Omits digressions, excessive formalities, and repetitive exercises.

- Provides exceptional preparation for probability and statistics courses.

- Includes problems (with all solutions) that extend your knowledge rather than merely reinforce it.

Contents

1. The Sum Rule and Product Rule

2. Permutations

3. Combinations

4. The Binomial Theorem

5. Combinations with Repetition

6. Summary and Solutions

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Tim Hill is a statistician living in Boulder, Colorado. He holds degrees in mathematics and statistics from Stanford University and the University of Colorado. Tim has written self-teaching guides for Algebra, Trigonometry, Geometry, Precalculus, Advanced Precalculus, Permutations & Combinations, Mathematics of Money, and Excel Pivot Tables. When he's not crunching numbers, Tim climbs rocks, hikes canyons, and avoids malls.