Do Now: Review 10.4 Multiple Choice 1.) What does mean? a.) b.) c.) Short Answer 2.) Find the number of arrangements of 3 #’s for a locker with a total of 35 options if: a.) all 3 numbers can be repeated b.) no numbers can be repeated
Algebra II Elements 10.5: Combinations Hw: p.548 (8-10, 12, 22, 24, 26, 28, 29)
Combinations • An ordering of r objects from a total of n objects where order is not important is a combination. • The number of combinations of r objects taken from a group of n distinct objects is denoted by n = total # of objects, r = how many you are taking
During the school year, the basketball team is scheduled to play 12 home games. If you want to attend at least 3 games, how many different combinations of games can you attend?
Combination or Permutation • A club has a president and vice-president position. Out of 12 students, how many ways can students be chosen for these two positions?
Combination or Permutation • Five representatives from a group of 120 students are to be chosen. In how many different ways can students be chosen as representatives?
Combination or Permutation A relay race has a team of 4 runners who run different parts of the race. There are 20 students on your track squad. In how many ways can the coach select students to compete on the relay team?
Combination or Permutation For summer reading, you are asked to read 2 books from a list of 6 books. How many different pairs of books can you choose to read?
Permutations, Combinations, and Probability • AND indicates multiplication • OR indicates addition
If you have a standard deck of cards, answer the following questions. • How many 5-card hands are possible?
From a standard 52-card deck, find the number of 5-card hands that contain the cards specified. 1.) 5 face cards 2.) 4 kings and 1 other card (not a king)
From a standard 52-card deck, find the number of 5-card hands that contain the cards specified. 3.) 1 ace and 4 cards that are not aces 4.) 5 hearts or 5 diamonds 5.) 5 red or 5 black