Transcript Chance of winning

Chance of winning
Unit 6 Probability
Multiplication Property of Counting

If one event can occur in m ways and
another event can occur in n ways, then
the number of ways that both events can
occur together is m·n. The principle can be
extended to three or more events
Example 1

At a sporting good store, skateboards are
available in 8 different deck designs. Each
deck design is available with 4 different
wheel assemblies. How many skateboard
choices does the store offer?
Addition Counting Principle

If the possibilities being counted can be
divided into groups with no possibilities in
common, then the total number of
possibilities is the sum of the numbers of
possibilities in each group.
Example 2

Every purchase made on a company’s
website is given a random generated
confirmation code. The code consists of 4
symbols (letters and digits). How many
codes can be generated if at least one
letter is used in each.
Finding Probabilities
Using Permutations
6.2 pg. 342
Vocabulary

Factorials- for any positive integer n, the
product of the integers from 1 to n is called n
factorial and is written n!. Except 0! Which is
equal to 1.
Examples

1. 6! = 6•5•4•3•2•1 = 720
Find:
 2. 10!
 3. 8!
Vocab.

Permutations- an arrangement of objects in which
order is IMPORTANT. The number of permutations
of n objects is given by
n n
  n!
Permutations

The number of permutations of n objects taken
r at a time, where r ≤ n, is given by:
n!
n r 
(n  r )!

Used for the arrangement of objects in a
specific order.
Examples
There are 5 students in the front row. How
many ways can I call on each of them to
present one of 5 problems on the board?
1st 2nd
3rd
4th
5th
5
4
3
2
1
So, I have 5•4•3•2•1 = 120 ways to call on them.
5 things taken 5 at a time… 5P5
4.
Example
What if we were choosing 5 people from the
entire class?
1st 2nd
3rd
4th
5th
30 29
28
27
26
5.
30!
30  29  28  27  26  25  ...

30 5 
(30  5)!
25  24  ...
So there are 17, 100, 720 ways to choose 5.
Example
6. A 3-digit number is formed by selecting
from the digits 4, 5, 6, 7, 8, and 9. There is
no repetition. How many numbers are
formed?
Example
7. How many of the numbers from Example 6
will be greater than 800?
Example
8. How many 3 digit numbers can be formed
using the digits 1, 2, 3, 4 and 5, if repetition
is allowed?
Example
9. How many different 4 letter words can be
formed from the word CALM?
(Assume any combo of 4 is a real word)
10. How many different 4 letter words can be
formed from the word LULL?
(Assume any combo of 4 is a real word)
What’s the difference in 9 and 10?
Permutations
The number of permutations of n things, taken n
at a time, with r of those things identical is:
n!
r!
11. How many different 4 letter words can be
formed from the word BABY?
Homework
Text book Pg. 344
2-26 even
Combinations
Section 6.3
Definition

A Combination is a selection of objects in
which order is NOT important. The number
of combination of n objects taken r at a
time, where r  n, is given by
n!
n Cr 
r ! n  r  !
Example

How many combinations of 3 letters from
a list of A, B, C, D are there?
Example

For your school pictures, you can choose 4
backgrounds from a list of 10. How many
combinations of backdrops are possible?
Example

Five students from the 90 students in your
class will be selected to answer a
questionnaire about participating in school
sports. How many groups of 5 students
are possible?
Homework
Page 349
 Numbers 2 -20 even
