Mathematics of Choice: Or, How to Count Without Counting

adjacent alike arrangements batches binomial binomial expansion blocks blue faces cards Chapter chromatic triangle circular permutations coefficient coins colors consider corresponds denote the number derangements dice are thrown distinct objects elements Evaluate example expansion factors Fibonacci Find the number five formula 5.3 four Hence the answer inclusion-exclusion principle integers satisfying interpretations least letters mathematical induction minus signs multiplication principle natural numbers non-negative integers number of distributions number of equally number of favorable number of objects number of partitions number of permutations number of regions number of solutions pairs Pascal's formula Pascal's triangle pigeonhole principle Pk+1 plane pn(n points positive integers preceding problem preceding question Problem Set property ẞ Prove selected separated sigma notation solutions in positive solutions of x1 subsets symbols telescoping sum things tions total number write zero Ν α