Algebra II

							       Algebra II
10.2: Use Combinations and the
       Binomial Theorem
            Combinations
 An ordering of r objects from a total of
 n objects where order is not important
 is a combination.
                 Combinations
   The number of combinations of r objects taken
    from a group of n distinct objects is denoted by
            and is given by the formula:




            n = total # of objects,
            r = how many you are taking
 Permutations, Combinations, and
           Probability

 AND    indicates multiplication

 OR    indicates addition
 Duringthe 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?
If you have a standard deck of cards,
    answer the following questions.
 How  many 5-card hands are possible
 if order is not important?



 How  many 5-card hands are possible
 if order is important?
If you have a standard deck of cards,
    answer the following questions.
 How  many 5-card hands of the same
  color are possible?
From a standard 52-card deck, find the
 number of 5-card hands that contain
         the cards specified.
 1.) 5 face cards
From a standard 52-card deck, find the
 number of 5-card hands that contain
         the cards specified.
 2.) 4 kings and 1 other card
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
From a standard 52-card deck, find the
 number of 5-card hands that contain
         the cards specified.
 4.) 5 hearts or 5 diamonds
From a standard 52-card deck, find the
 number of 5-card hands that contain
         the cards specified.
 5.) at most 1 queen
From a standard 52-card deck, find the
 number of 5-card hands that contain
         the cards specified.
 6.) at least 1 spade
     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
 Fiverepresentatives from a group of 280
 students are to be chosen. In how many
 different ways can students be chosen as
 representatives?