## CountingThis book is a useful, attractive introduction to basic counting techniques for upper secondary and junior college students, as well as teachers. Younger students and lay people who appreciate mathematics, not to mention avid puzzle solvers, will also find the book interesting. The various problems and applications here are good for building up proficiency in counting. They are also useful for honing basic skills and techniques in general problem solving. Many of the problems avoid routine and the diligent reader will often discover more than one way of solving a particular problem, which is indeed an important awareness in problem solving. The book thus helps to give students an early start to learning problem-solving heuristics and thinking skills. |

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I have read many books on counting (permutation and combination) but what I read in this book is awesome and exact.

Excellent book for basic and advanced knowledge

### Contents

The Addition Principle | 1 |

The Multiplication Principle | 9 |

Subsets and Arrangements | 17 |

Applications | 25 |

The Bijection Principle | 35 |

Distribution of Balls into Boxes | 47 |

More Applications of BP | 53 |

Distribution of Distinct Objects into Distinct Boxes | 63 |

Other Variations of the Distribution Problem | 67 |

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### Common terms and phrases

5-member committee 6-digit binary sequences Addition Principle adjacent answer applying Bijection Principle binomial coefficients Binomial Expansion Blaise Pascal box can hold boys Chapter choices choose chords chosen circle Combinatorics coprime correspondence count the number counting problem denote desired number digit distinct boxes distinct objects distribute r identical Distribution of Distinct distribution problem elements establishes a bijection exactly Example expressed Find the number finite sets girls given identical balls identical objects Jia Xian lattice point mapping Multiplication Principle n-element set natural number nonnegative integer solutions number of arrangements number of integers number of positive number of r-element number of r-permutations number of shortest number of triangles ordered pairs palindrome Pascal's Triangle persons points of intersection positive integer r-element subsets required number shortest P—Q route shown in Figure smallest member solve squares subsets of Nn surjective ternary sequences vertices X—D routes