The Math Forum

For anyone with a love of math
 
HomeHome  CalendarCalendar  GalleryGallery  FAQFAQ  SearchSearch  MemberlistMemberlist  UsergroupsUsergroups  RegisterRegister  Log in  

Share | 
 

 Counting Lesson 2

View previous topic View next topic Go down 
AuthorMessage
Dojo
Admin
Admin
avatar

Number of posts : 154
Location : Probably somewhere near a computer
Registration date : 2008-08-12

PostSubject: Counting Lesson 2   Tue Aug 19, 2008 11:04 pm

Yay!!! We continue the lessons of Counting.
Today we will do basic counting of certain objects.

Example 1:
How many ways can you arrange the letters in the word: WORD.
Lets see how to figure this question out.
For the first letter, there are 4 possiblities, W, O, R or D.
So 4 _ _ _
Now we have 3 left over:
4 3 _ _
And it continues to 4,3,2,1, which is 24.
This is also known as factorials.
4! (!=factorial) =24
W-O-R-D
W-O-D-R
W-R-O-D
W-R-D-O
W-D-O-R
W-D-R-O
continued...

Here is a table of some factorials.
1!=1
2!=2
3!=6
4!=24
5!=120
6!=720
7!=5040
...

Now lets look at another problem.

Example 2:
Coins.
How many outcomes are there for 3 coins?
For the first coin, we either have a head or a tail. (H,T)
Using the same method as above, we have 2x2=4
These are just powers of 2.

_________________
~Dojo
Back to top Go down
View user profile http://themathforum.forumotion.com
AIME15
Hardcore TMF user
Hardcore TMF user
avatar

Number of posts : 163
Age : 21
Location : Pleasanton, CA
Registration date : 2008-08-13

PostSubject: Re: Counting Lesson 2   Wed Aug 20, 2008 1:31 pm

What if the word is something like HAPPY? Denote the first P as P_1 and the second one as P_2. So we would count as HAP_1P_2Y and HAP_2P_1Y as different things, even though they're both HAPPY. There is a principle: If there are n letters total, and k letters are repeated, the amount of permutations is n!/k!, because each repeated thing is counted k! times. So our answer would be 5!/2!, or 120/2=60.
Back to top Go down
View user profile
Dojo
Admin
Admin
avatar

Number of posts : 154
Location : Probably somewhere near a computer
Registration date : 2008-08-12

PostSubject: Re: Counting Lesson 2   Wed Aug 20, 2008 9:36 pm

This will be explained in overcounting.

_________________
~Dojo
Back to top Go down
View user profile http://themathforum.forumotion.com
AIME15
Hardcore TMF user
Hardcore TMF user
avatar

Number of posts : 163
Age : 21
Location : Pleasanton, CA
Registration date : 2008-08-13

PostSubject: Re: Counting Lesson 2   Thu Aug 21, 2008 12:07 am

All right, I didn'tknow that Very Happy sorry
Back to top Go down
View user profile
Sponsored content




PostSubject: Re: Counting Lesson 2   

Back to top Go down
 
Counting Lesson 2
View previous topic View next topic Back to top 
Page 1 of 1
 Similar topics
-
» Counting Down
» Clarification on when to start the counting of contract period.
» Lesson Eight- The Obligatory Elements of Prayer
» Lesson Plan : Back to Nature by Mrs. Kobzili Z.
» 4 A.M Lesson Sheet Preparation : File 01

Permissions in this forum:You cannot reply to topics in this forum
The Math Forum :: Dojo's Math Encyclopedia (Unfortunately sadly small) :: Counting & Probablilty-
Jump to: