For your upcoming test:
- Know how to verbally and mathematically describe a set
- Know the definition and how to use unions, intersections, and complements
- Know how to represent set(s) with a Venn diagram
- Know how to shade the appropriate region of a Venn diagram corresponding to a given set
- Know how to use the principle of inclusion-exclusion for counting
- Know how to find the number of objects in a each of the non-overlapping regions of a circle Venn diagram
- Know how and when to use multiplication in counting
- Know the definition of C(n,k), and its formula
- Know Pascal’s Identity: C(n,k) = C(n-1,k) + C(n-1,k-1)
- C(n,k) counts k-element subsets of the the set {1,2,..,n}. Which of these subsets are counted by C(n-1,k-1) in Pascal’s Identity.
- You should be able to use Pascal’s triangle to compute various C(n,k)
- Know when a counting problem involves counting subsets
- Examples:
- Selecting balls and putting them in a box
- Handshakes
- Number of matches in a league
- Many many more!
- n coin tosses with exactly k heads (see Section 5.6)
- Routes through a city (see Section 5.6)
- Examples:
- When counting routes in a city (see Section 5.6): Given a route you should be able to write down the subset that corresponds to it.
In general, the best thing to do to study for this test is to review the examples from lecture and homework. The more practice you have, the better you’ll be able to handle the questions on the test!