Permutation & COmbination Warm up: 1. Suppose a pizza parlor offers pizzas in three different sizes—small, medium, and large. If there are 10 different toppings to choose from, how many different one-topping pizzas could you order? 2. A club has nine members. In how many ways can a president, vice president, and secretary be chosen from the members of this club?
Homework Questions:
How do we differentiate when to use permutation or combination rules? Idea of the day How do we differentiate when to use permutation or combination rules?
Investigation: How many choices do I have? Given a King, a Jack, a Queen, and an Ace Task 1: Students are to pick two cards at a time order does mater. How many possible ways can a student pick 2 cards? Write down your sample space Assume that order does not matter this time look at your sample space that you’ve just collected. How many possible ways can the student pick two of the same card
Investigation: How many choices do I have? Given a King, a Jack, a Queen, and an Ace Task 2: Now let’s pick three cards from the four that are given, assuming order does matter. How many possible ways can a student pick three cards? Write down your sample space Assuming order doesn’t matter this time. How many ways can a student pick three cards?
What conclusion can you make? Group Discussion: What have you notice about your sample space on the matter of whether or not order matter? What conclusion can you make?
Put your name down on a sheet of paper and alphabetize it Ambassador Game: Put your name down on a sheet of paper and alphabetize it The person who’s ______________ and ___________ go to a different group Then discuss what you’ve discover to see if you all are in agreement with your conclusion
Review: Different Methods There are 3 methods for calculating the number of possible outcomes for a sequence of event. Counting Rules Permutation Rules Combination Rule
Review: Counting Principle: Suppose that two events occur in order. If the first can occur in “m” ways and the second in “n” ways (after the first has occurred), then the two events can occur in order in m x n ways. Order is extremely important for the counting principle. In simple words, multiply the number of possibilities for each individual event
Review Factorial:
Permutations A permutation of a set of distinct objects is an ordering of these objects. Used for an arrangement of object that are in specific order The number of permutations of n objects is n!
Example For example, here are some permutations of the word “THEIS”: SIEHT HEIST HTSEI TISEH etc.
Example: A club has nine members. In how many ways can a president, vice president, and secretary be chosen from the members of this club?
Permutations of n objects taken r at a time The number of permutations of n objects taken r at a time is: On your calculator, permutations are written as nPr and are found under MATHPRB.
Examples: How many different ways can a chairperson and an assistant chairperson be selected for a research project if there are seven scientists available?
Examples: How many permutations can be formed from the word “Justice” using only 5 letters?
Example: From a group of 9 different books, 4 books are to be selected and arranged on a shelf. How many arrangements are possible?
Combinations Used for an arrangement of objects with No specific order Order doesn’t matter
Combinations The formula for computing a combination of n objects taking r at a time is: On your calculator, you can use nCr which is located under MATHPRB
Example: How many combinations of the letter A,B,E,H,L and P are there if they put in groups of 2s?
Example: At the hamburger Hut you can order hamburgers with cheese, onions, pickles, relish, mustard, lettuce or tomato. How many different combinations of the “extras” can you order, choosing any 3 of them?
Example: In a club there were 7 women and 5 men. A committee of 3 women and 2 men is to be chosen. Hoe many different possibilities are there?
Revisiting the EQ: How do we differentiate when to use permutation or combination rules?
Class work Section 13.2 AFM Book Page 888-891 #1-66 odd
Permutation and Combination Homework