## November 22, 2006

### Countings and Combinations

Hi im John,the scribe for today.
In today's class, we started our lesson about a chance of winning 6/49 lotteries.
Mr. K explain to us our chance to win in the lottery. i'll give you some of his explanation.
In 6/49, we have to choose 6 numbers in order for us to get the ticket.
Here is the explanation in the problem.
Assuming there's 49 letters word, 6 of that is the one we like and the rest are those we doesn't chose..

49 C 6 = 49! / (49-6)! 6!
= 49! / 43!*6!
= 13,983,816 no. of ways tickets can be sold in lotto 6/49.
So, if you buy 1 ticket: 1 / 13,983,816 is your chance.
: 7.15 x 10^-8
: 0.0000000715 % a chance in choosing a number in lottery.

He ask the class, do you still buy a lottery? For me, Yes. I will. because still i have a single chance to win in the lottery and maybe that's the time what I'm waiting for.
Anyway, back into class..
If we have 20 people, can we still do to become a lottery winner assuming the pot money is 14 million or above.?
let say, every 15 sec. is the time of processing the ticket.
so 15*4 is 60.this is minutes.
60mins = 1 hour therefore 24x60 = 1440 tickets can be print in an hour.
1440 x 24 = 34560 because we're looking for day.
the answer multiply by 20 people equals 691200.
therefore:
13983816 / 691200 = 20.23121528
We say that there are 20 days will take to get the lottery card to finished.

Again, the question is, are u still going to buy a ticket because there's just 4 days to wait before the 6/49 drawn..

EXPECTED VALUE:
P(WIN)*GAIN + P(LOSE) *LOSS
G + L = 0.9284886
Everytime we play lotto we loss 0.9284886 cents.

JOKE TIME:
There is a mathematician guy, i forgot his name, always thinking "there is a bomb in a plane." but when he go to plane, he says "there is 2 bomb in a plane." so Every time he flies he brings a bomb.

MATH DICTIONARY

COMBINATIONS : An arrangement of objects where order does not matter.

NOTATIONS: n C r or (r/n)
> means from a set of n objects, how many different groups of r objects can be chosen where order doesn't matter.

FORMULA: n C r = n! / (n-r)! r!

EXAMPLE:
How many tickets can be sold in the 6/49 lottery?

49 C 6 = 49! / (49-6)! 6! OR
= 49 / 43!6!
= 13,983,816 ways ticket can be sold.

we ask to solve the problem:

How many different ways can a group of 3 students be selected from 7 students?
Solutions:
7 C 3 = 7! / 4!3!
= 7*6*5 / 3*2*1
= 35 ways

A sample of 5 people are selected from 3 smokers and 12 non-smokers. In how many ways can the 5 people be selected?
Solutions:
15 C 5 = 15! / 10!5!
= 15*14*13*12*11 / 5*4*3*2*1
= 3003

You have a penny, nickel, dime, quarter, loonie and toonie in your pocket. If you pull out a 3 coins, how many different sums are possible?
Solutions:
6 C 3 = 6! / 3!3!
= 6*5*4 / 3*2*1
= 20

Ten people, including one married couple, are eligible to attend a conference, four people can go and the married couple only go as a pair. How many different groups of 4 can go?
Solutions:
> 10 C 4 if the couple split them up
>8 C 4 if the couple is the problem
there is only 1 way to send the couple
8 C 2 is the other people
therefore:
8 C 4 + 1 * 8 C 2 = 98 ways

GROUP PROBLEM

FOOTBALL
There are 10 football teams in a certain conference. How many games must be played if each team is to play every other team just one?
Solution:
9+8+7+6+5+4+3+2+1 = 45 or

10 C 2 = 45

PRESENTS
a.) In how many ways can 9 presents be given to two children?
9 C 2 = 9! / (9-2)! 2!
= 36

b.) In how many of these ways will younger child recieve just 5 presents?
9 C 5 * 4 C 4 = 126*1
=126 ways

Seven people reach a fork in a road. In how many ways can they continue their walk so that 4 go one way and 3 the other?
solution:
7 C 4 * 3 C 3 = 35
7! / 4!3! 3! / (3-3)! 3!
= 35 ways

POINTS
there are 9 points marked in a plane.No three of which lie in a straight line.
a.) How many straight lines can be drawn,each containing 2 of the points?
solution:
9 C 2 = 36

8+7+6+5+4+3+2+1 = 36 straight lines

b.) How many of these pass through one or more of 3 specified points in the set?
solution:
8+7+6 = 21 ways

classmate, i forgot to ask the 2nd group problem to my groupmate this afternoon because we're running out of time. Because you know i'm having a hard time to understand the lesson thats why i have to listen to the explanation of Mr. K. Im going to post it tomorrow.

If you dont understand my post, you can talk to me anytime.
THANKS.. I'll choose ASHLEY to be the next scribe.