Sections, concepts, and problems

4.1. The basics of counting. The sum rule, the product rule, the inclusion-exclusion principle, and some (rooted) trees.
1, 3, 5, 15, 17 [Note. The answer is n-m where n is the total number of strings and m is the number of strings that have 0 @-signs.], 23, 25, 29a-e [for (e), see the note to 17 above], 37, 39a

4.2. The Pidgeonhole Principle. The Pidgeonhole Principle and applications.
5, 9, 11 [Hint. The midpoint of (a,b,c) and (d,e,f) has integer coordinates iff a and d are both even or odd, b and e are both even or odd, andc and f are both even or odd.], 15, 25

4.3. Permutations and Combinations. r-permutations, r-combinations, the Binomial Theorem, Pascal's identity, Pascal's triangle.
1, 5a, 7, 9, 11, 15, 19, 25, 31, 37, 55 [for (b), choose the n locations of the 0's from the n+m possible spots]

Other Chapters

Chapter 1 | Chapter 2 | Chapter 3 | Chapter 4 | Chapter 6