## Wednesday, May 7, 2008

### THE MiTSUBISHSONYTOSHIBaHONDATOYOTASAmSUNG PLAYSTATION PANASONIcCASIoJVCCLARIonYAMAHAAAAFUJIKODAK SANYOHITACHI.. BlOG

Well first off.. I'd just like to say that this blog isn't entirely all about japanese brands, or brands that sound japanese. Here's a little guide line of what I will be discussing in this blog. (Again sorry if it is late for you early birds.)

#1) THE NEXT SCRIBE WILL BE .. Zeph! .. cool hey?! Just returning the favor.

#2) Poker Combinations

#3) Pre-Test Thoughts

#4) Conic Sections

.. Because #1) is said, #2) is automatically first.

Instead of starting the class with the pre-test, which was how it was supposed to be scheduled. We discussed last night's homework instead.
Poker hands consist of 5 cards.

We started with the FLUSH.
A flush is getting any card in any order, but all 5 cards having the same suit.
So we use 13C5 to pick 5 cards in 1 suit.
4C1 to pick all cards in 1 suit
and because we are only looking for flush NOT INCLUDING straight flushes and royal flush.
We would subtract 4x10, because that's all the ways for straight flushes and royal flush.
4C1*13C5-40 = 5108

Next we have the STRAIGHT.
A straight is an order of 5 face cards. A, 2, 3, 4, 5 is an example. A can be low and high.
10 is the number of ways we can have the cards in sequence.
[A,2,3,4,5](1),6(2),7(3),8(4),9(5),10(6),J(7),Q(8),K(9),A(10)
we would want to avoid having the same suit, because then it would be a STRAIGHT FLUSH.
So we have 10, the number of ways we can have the cards in sequence.
4C1 to pick each card for it's suit.
(4C1)^5 because there are 5 cards.
40 is the number of straight flushes.

(4C1)^5 * 10 - 40 = 10200

Next we have the 3 of a kind!
As the name says, 3 face cards of the same kind. 2 other random face cards.
So we have 13C1 to pick 1 face card for the 3 first cards.
4C3 to pick the suits (Can't have 3 of the same suit and face card.)
12C2 to pick 2 more face cards.
(4C1)^2 for the suits of the other 2 cards. (Making sure they are all different suits.)

13C1 * 4C3 * 12C2 * (4C1)^2 = 54912

After 3 of a kind, we have 2 pairs!
A pair means 2. And 2 pair means another 2. So we need 2 cards of the same face card, and another 2 cards with the same face card. And a random 5th.
So we have 13C2 for picking 2 face cards for 2 pairs.
4C2 for picking 2 different suits for the 2 pairs.
11C1 is for the 5th card.
4C1 is for the 5th card's suit.

13C2 * 4C2 * 4C2 * 11C1 * 4C1 = 123552

If we can have 2 pairs, then there must be 1 pair!
Meaning 2 cards of the same face card. Then 3 random 3. Heh that's catchy.
So we have 13C1 to pick 1 card for the pair.
4C2 for the two cards.
12C3 for the other 3 cards.
(4C1)^3 for the suits of the other 3 cards.

13C1 * 4C2 * 12C3 * (4C1)^3 = 1098240

If we do not have any of those .. No pairs.
Although this may seem to be the easiest one to figure out, it was actually the most confusing for the class.
First, we know we can have any card that is not the same, in no order and are all different.
13C5 * (4C1)^5 is the ways to have all different face values.
13C1 * 4C1 is the ways to have all the cards same suit (FLUSH).
10 * (4C1)^5 - 10*4 is the ways to have all cards in sequence.

13C5 * (4C1)^5 - 13C1 * 4C1 - (10 * (4C1)^5 - 40) = 1307428

That is the end of the poker combinations! Now to move on to ..

#3) Pre test ..

Mr K. said there was only one problem that everyone had a problem on. That question was number 4!
"A multiple choice exam has 20 questions each with four possible answers, and 10 additional question, each with five possible answers. How many different answer sheets are possible?"

Each of the 20 questions has 4 possible answers. 1 - 4, 2 - 4, 3 - 4, etc ...
Each of the 10 questions has 5 possible answers. 1 - 5, 2 -5 etc ...
4^20 + 5^10
= 1099511627776 + 9765625
= 1099521393401

Now moving on to the .. very wild afternoon ..
So starting off .. It kinda took a while for everyone to settle down. When we finally did. Mr K. just couldn't help it. He was turning into a tomato! With all our japanese sounding words .. and .. His very bad dubbing .. And the cow bell was it ? eh anyways ..

#4) The Conic Section
How do I explain this? Mr. K used his lightning fast skills and chopped off a cone. Yes A CONE! To show us where the circle, parabola, ellipse and hyperbola came from. As also shown in SLIDE 2.
ANNND THENNNNN .. because my lack of sleep I began to fall asleep.

Next Mr. K kindly handed out some nice white paper for an experiment on our own. Of course skipping all the laughter and stupid jokes popping out of our mouths. Especially something about hamburgers and hotdogs. Going on ..

REFERRING TO SLIDE 3 ..

We found where the parabola comes from. It is curved by the FOCUS POINT ..
Then, on our parabola, we were asked to place another point on the parabola and call it p, and then draw a vertical line from P to the edge of our paper, which is the DIRECTRIX. Then connect P to F. We found out that PD is the same length as PF .. Yay! We know where the vertex is.. It has the same X coordinate of the focus point. Also the lengths in between F and V and V and D are the same. We call this line lower case p.
The Vertex having the coordinates (H,K)
Then the focus point must have the coordinates (H, K + P)
Ya'll Dig? ..
Then that must mean the Directrix must have the coordinates .. (H, K - P)
We don't know P's coordinates, which is why it is (X, Y)

So we know PD is equal to PF .. The unit will continue.

And that's all! One again the Scribe is ZEPH. Good luck on the test everyone. I know I'LL need it.

Cheers!