Algebra IIAlgebra II

10.2: Use Combinations10.2: Use Combinations

Quiz 10.1-10.3: Friday, 12/13

CombinationsCombinations An ordering of An ordering of rr objects from a total of objects from a total of nn objects where order is not important objects where order is not important is a combination.is a combination.

The # of combinations = where The # of combinations = where n = total # of objects, r = # you n = total # of objects, r = # you are taking.are taking.

p.691 example 3: During the school p.691 example 3: During the school year, the basketball team is scheduled year, the basketball team is scheduled to play 12 home games. If you want to to play 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

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

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

Combination or PermutationCombination or Permutation p.695 #39: Five representatives from a p.695 #39: Five representatives from a

group of 280 students are to be chosen group of 280 students are to be chosen for members of student council. In how for members of student council. In how many different ways can students be many different ways can students be chosen?chosen?

Combination or PermutationCombination or Permutation p.695 #40: A relay race has a team of p.695 #40: A relay race has a team of

4 runners who run different parts of the 4 runners who run different parts of the race. There are 20 students on your race. There are 20 students on your track squad. In how many ways can the track 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?

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?

How many 5-card hands of the How many 5-card hands of the same color are possible?same color are possible?

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

cards specified.cards specified.1.) 5 face cards1.) 5 face cards

2.) 4 kings and 1 other card2.) 4 kings and 1 other card

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

cards specified.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

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

cards specified.cards specified.5.) at most 1 queen5.) at most 1 queen

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

cards specified.cards specified.6.) at least 1 spade6.) at least 1 spade