Mathematics of Choice Or how to Count Without Counting

adjacent alike arrangements batches binomial Binomial Coefficients binomial expansion blocks blue faces cents Chapter chromatic triangle circular permutations coefficient coins colors compute consider corresponds denote the number derangements distinct digits distinct objects elements Evaluate example expansion factors Find the number five formula 5.3 four Hence the answer inclusion-exclusion principle inclusive integers satisfying interpretations mathematical induction minus signs multiplication principle natural numbers non-negative integers notation number of distributions 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 polynomial positive integers possible preceding problem preceding question Problem 2.3 Problem Set Prove selected seven sigma notation solutions in positive solutions of x1 solved symbols telescoping sum things tion total number types values write zero Ν α