Do Now: Review 10.4Do Now: Review 10.4Multiple ChoiceMultiple Choice

1.) What does mean?1.) What does mean?

a.) a.) b.) b.) c.) c.)

Short AnswerShort Answer

2.) Find the number of arrangements of 2.) Find the number of arrangements of 3 #’s for a locker with a total of 35 3 #’s for a locker with a total of 35 options if:options if:

a.) all 3 numbers can be repeateda.) all 3 numbers can be repeated

b.) no numbers can be repeatedb.) no numbers can be repeated

335P353535 333435 123

Algebra II ElementsAlgebra II Elements10.5: Combinations10.5: Combinations

Hw: p.548 (8-10, 12, 22, 24, 26, 28, 29) Hw: p.548 (8-10, 12, 22, 24, 26, 28, 29)

CombinationsCombinations An ordering of An ordering of rr objects from a total of objects from a total of nn

objects where objects where order is not importantorder is not important is is a combination. a combination.

The number of combinations of The number of combinations of rr objects objects taken from a group of taken from a group of nn distinct objects is distinct objects is denoted by denoted by

n = total # of objects, r = how many you are taking

During the school year, the During the school year, the basketball team is scheduled to play basketball team is scheduled to play 12 home games. If you want to 12 home games. If you want to attend at least 3 games, how many attend at least 3 games, how many different combinations of games can different combinations of games can you attend?you attend?

Combination or PermutationCombination or Permutation A club has a president and vice-A club has a president and vice-

president position. Out of 12 president position. Out of 12 students, how many ways can students, how many ways can students be chosen for these two students be chosen for these two positions?positions?

Combination or PermutationCombination or Permutation Five representatives from a group of Five representatives from a group of

120 students are to be chosen. In 120 students are to be chosen. In how many different ways can how many different ways can students be chosen as students be chosen as representatives?representatives?

Combination or PermutationCombination or Permutation A relay race has a team of 4 runners A relay race has a team of 4 runners

who run different parts of the race. who run different parts of the race. There are 20 students on your track There are 20 students on your track squad. In how many ways can the squad. In how many ways can the coach select students to compete on coach select students to compete on the relay team?the relay team?

Combination or PermutationCombination or Permutation For summer reading, you are asked For summer reading, you are asked

to read 2 books from a list of 6 to read 2 books from a list of 6 books. How many different pairs of books. How many different pairs of books can you choose to read?books can you choose to read?

Permutations, Combinations, Permutations, Combinations, and Probabilityand Probability

AND AND indicates multiplication indicates multiplication

OR OR indicates addition indicates addition

If you have a standard deck of If you have a standard deck of cards, answer the following cards, answer the following

questions.questions. How many 5-card hands are How many 5-card hands are

possible?possible?

From a standard 52-card deck, From a standard 52-card deck, find the number of 5-card hands find the number of 5-card hands that contain the cards specified.that contain the cards specified.

1.) 5 face cards1.) 5 face cards

2.) 4 kings and 1 other card (not a 2.) 4 kings and 1 other card (not a king)king)

From a standard 52-card deck, From a standard 52-card deck, find the number of 5-card hands find the number of 5-card hands that contain the cards specified.that contain the cards specified.

3.) 1 ace and 4 cards that are not 3.) 1 ace and 4 cards that are not acesaces

4.) 5 hearts or 5 diamonds4.) 5 hearts or 5 diamonds

5.) 5 red or 5 black5.) 5 red or 5 black