Counting Project
- 1. Counting & Bases Chapter 12 & Chapter 4.3 BY: Gessica, Crystal, Israel, and Quentin
- 2. Counting Methods We can count a set by listing its elements systematically. We can use tree diagrams to help visualize counting situations. We can solve counting problems by imagining a tree instead of drawing it
- 3. Counting sets by listing One of the simplest ways to count a set is to list its elements. Examples: A. Flip a coin a) two ways: Heads or Tails.
- 4. Tree Diagram Tree diagram is handy way to illustrate the possibilities. How many ways can three coins be flipped??
- 5. … cont’d Forming two letter words using D and B. how many ways can it be formed? Depends if repetition is allowed or not.
- 6. Dice Set To emphasize that the dice are different, we assume that one is purple and the other is green. Clearly a 2red and a 3green is not the same as a 2green and 3red. We use ordered pairs There are 36 pairs from a pair of dice
- 7. The Fundamental Counting Principle If we wish to perform a series of task and the first task can be done in A ways, second B ways, and third C ways.. Task can be done in A x B x C ways.
- 8. FCP in Coin and Dice Problems. How many ways can a four coins be flipped? - two ways possible. 2 x 2 x 2 x 2 = 16 ways! How many ways can three dice (red, blue, green) be rolled? -rolling die can be done 6 ways. 6 x 6 x 6 = 216 ways!
- 9. Permutation A permutation is an ordering of distinct objects in a straight line. P(n, r) : given “n” objects and selecting “r” of them. Formula for computing P(n, r) - P(n, r) = n! Divided by (n – r)
- 10. combination A combination is a set of objects in which order is not imporant
- 11. Factorial Notation! Factorial notation is often used in questions in combinatorics. It is when you need to multiply consecutive numbers. When you see x ! it is the factorial of x that is being asked for. When asked to calculate the following 7! your solution will look something like: 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040. Your calculator will have a key that will perform this operation for you.