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.

Chance of winningUnit 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:

Used for the arrangement of objects in a specific order.

!( )!n rnn r

Examples

4. 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 1So, I have 5•4•3•2•1 = 120 ways to call on

them. 5 things taken 5 at a time… 5P5

Example

5. What if we were choosing 5 people from the entire class?

1st 2nd 3rd 4th 5th

30 29 28 27 26

So there are 17, 100, 720 ways to choose 5.

30 530! 30 29 28 27 26 25 ...

(30 5)! 25 24 ...

Example6. 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?

Example7. How many of the numbers from Example

6 will be greater than 800?

Example8. How many 3 digit numbers can be

formed using the digits 1, 2, 3, 4 and 5, if repetition is allowed?

Example9. 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?

PermutationsThe number of permutations of n things,

taken n at a time, with r of those things identical is:

11. How many different 4 letter words can be formed from the word BABY?

!!nr

HomeworkText book Pg. 344

2-26 even

CombinationsSection 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

n

, is given by!

! !r

r nnC

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