Algebra II

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```							       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?

```
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