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Tuesday, February 28, 2006 

Scribe

Hi it is me. i hope none of you knows me.I am today's scribe and here are details of what we did in class today.
1) Factorial Notation:
Definition:- n!=n(n-1)(n-2)(n-3)......3-2.
0!=1
Examples: 4!=4.3.2.1 6!=6.5.4.3.2.1
= 24 =720

on the TI83: 6! then punch 6 on the main screen then press(Math) then (<) then(4) then (Enter) Note: Factorial notation is not defined for negative numbers. i.e (-3)! is undefined. Permutation: A permutation is an ordered arrangement of objects. Formula: nPr=n1/(n-r)! [often called the "pick" formula] n is the number of objects to choose from r is the number of objects to be arranged nPr is read as: 1)"n permute r" OR 2) "n pick r" nPr means: Given a set of n objects. How many different arrangements can you make using only r of them at a time. Example 1) 6P2=6!/(6-2)!
=6!/4!
=6.5.4.3.2.1/4.3.2.1
=6.5
=30

Example 2) There are 8 horses in a race. In how many different ways can they finish 1st, 2nd and 3rd?
Solution 1): By the fundamental principle of counting.
8.7.6=336
Solution 2): As a permutation
8P3 = 8!/(8-3)!
=8!/5!
= 8.7.6.5.4.3.2.1/5.4.3.2.1
= 336
Permutations of Non-Distingiushable objects.
The number of ways to permute n objects which contain K1,K2,K3......... Non-Distinguish object is given by:
n!/K1!K2!K3!
Example: How many different "words" can be made from the letters of the word:
a)Book b) Mississippi
#Letters:4 #Letters:11
#o,s : 2 #I,s:4
4!/2! #S,s:4
4.3.2.1/2.1 #P,s:2
=12 11!/4!4!2!
=34650.
All the above are notes that we copied down in to our dictionaries today.(Good luck With That)

And Further more:I expect every one to know the meaning of permutation(Means That order Matthers)
That is all important stuff we did in class today.
We also found out the probability of winning 649.
If you had to pick from 49 factorial Y=yes N-No (NNN............YYYYYY)
The formula to find the probability = 49!/6!43!=13983816
which shows that the probability of winning a 649 is 1 out of 13983816 (This is a code word Which means don,t waste money on lotto 649)
Homework: Page 23 Question 1-6.
Thats all for today folks.

Note: Sorry i forgot to choose scribe for tomorrow.
Jessica is tomorrows scribe.




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Good scribe post Khan!

You covered the material very well. It would be a little easier to read if you had an extra space between each paragraph. But I really liked the amount of detail. The best part was when you explained about the "code word." ;-)

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