245 Chapter 4 Outline

Sections, concepts, and problems

Section 1. Getting from Point A to Point B. Combinations, Pascal's triangle, the Binomial Theorem, and some basicidentities involving combinations.
1 (leave your answer in terms ofnCk), 2 (leave your answer in terms of nCk), 4 (leave your answer in terms of nCk) Hint: I think 2310 is the product of the first five primes, 6a, 6d, 7 (explain the answer in the book)

Section 2. Set The Fundamental Principle of Counting. The fundamental counting principle, permutations of n objects taken k at a time, and a bunch of examples.
2, 4b, 6, 7abd, 8a, 8b

Section 3. A Formula for the Binomial Coefficients. Just like it says.
3bd, 5, 6, 7b, 8, 10 (why?)

Section 4. Combinatorics with Indistinguishable Objects. How to count ordered and unordered arrangements if some of the objects look the same as some others.
1f, 5, 9, 11ab, 14, 15

Section 5. Probability. The notion of basic discrete probability and some examples.
1, 4a, 4d, 6a, 8 (use prime factorization), 10b (see Example 4.5.4)