Notes 10.1 Apply the Counting Principle and Permutations
Tree Diagrams!! A sporting goods store offers 3 types of snowboards (all-mountain, freestyle, and carving) and 2 types of boots (soft and hybrid). How many choices does the store offer for snowboarding equipment? (Solve by using a tree diagram)
VOCAB!! Event – An outcome The Fundamental Counting Principle - MULTIPLY THE NUMBER OF EVENTS!!!! DO NOT ADD.
Directions: Use the counting principle to find the number of possible outcomes. Choosing lunch from 4 sandwiches, 3 drinks and 5 desserts Choosing an outfit from 2 jackets, 3 pairs of pants, and 4 shirts Choosing a pizza with tomato, pesto or cheese sauce and a topping of mushroom, meat or eggplant
Use the Fundamental Counting Principle. You are framing a picture. The frames are available in 12 different styles. Each style is available in 55 different colors. You also want blue mat board, which is available in 11 different shades of blue. How many ways can you frame the picture?
Use the counting principle with repetition. The standard configuration for a Texas license plate is 1 letter followed by 2 digits followed by 3 letters. • How many different license plates are possible if letters and digits can be repeated? • How many different license plates are possible if letters and digits cannot be repeated?
Permutation: • A statistical analysis in which ORDER DOES MATTER!! Written as: nPr Factorial ! Calculate: 3! 6! 2! 4! 0!
Permutations: (nPr) nPr Find: • 7P5 • 4P4 • 2P0 5P2 3P1
Find the number of permutations. Ten teams are competing in the final round of the Olympic four-person bobsledding competition. • In how many different ways can the bobsledding teams finish the competition? • In how many different ways can 3 of the bobsledding teams finish first, second, and third to win the gold, silver, and bronze medals?
Find the number of permutations. You are burning a demo CD for your band. Your band has 12 songs stored on your computer. However, you want to put only 4 songs on the demo CD. In How many orders can you burn 4 of the 12 songs onto the CD?
Permutations with repetition!!! When dealing with permutations of words, it can be impossible to tell which letters you have already used. For example, using these letters, P, O, O, P, Y, how many different words can we make? We know that we should have 5P5. However, how can you tell the difference between POOPY and POOPY? No, POOPY is POOPY is POOPY. So, this is what you have to do.
Distinguishable Permutations! You take 5P5, but divide it by the factorial of anything repeated or “indistinguishable”. So in this case, we have 5P5 divided by (2! (for the P) times 2! (for the O)). Find the number of permutations of three letter words using E, E, and Y.
Find the number of distinguishable permutations of the letters in • MIAMI • TALLAHASSEE • MALL • KAYAK
Homework: P 686 3-16, 18-41, 43-54, 62-67