## Wednesday, May 13, 2009

### BOB!!!! (OBB, BBO, xD)

Wow time just flies doesn't it? We're already almost done another unit! And you know what that means......It's time to let the BOBs FLY!!!! So now I have decided to release my BOB and let it fly freely across the web. Here we go!

OK, so Combinatorics, it was fairly easy. I finally got to use that wonderful "!" key on my calculator and I got to write it down so many times. I thought that the most easy part about this was actually the "Pick" and "Choose" formulas and using the factorials ("!"). Yea, I guess you could call that three things, but they were all still pretty easy. Once I found out how and when to use each formula, I found them pretty easy to use and remember. The factorials were really helpful in keeping my work clean, short and most of all ELEGANT!! (lol.)

The hardest parts came when the "tricky" word problems arose from their long slumber in Mr.K's Smart Board lessons. I just really need to learn to really carefully read the questions and think about the scenarios. I also need to just relax and keep my cool. If I lose it, then I'll over think and miss little important details. To be honest, it was just today that it dawned on me that this unit could actually be very confusing and difficult. Then again, it could just be me. I do feel that after today (after struggling), I think I feel more confident about these kinds of questions.

The test? Yea I think I'll do well. Actually (and I hope I don't jinx anything by saying this), I feel like I'm going to blow this test out of the water and make it beautifully arch before going back into the water. I'll let you interpret what I just said. Haha, let your imaginations go wild!

Well now's about the time that I give the advice right? Let's start!

1. Permutations are when the order matters (medal standings, picking president/vice president/secretary of a committee, PERMUTATION (not combination) locks). If it's a permutation, then use the "pick" formula: nPr=(n!)/(n-r)!
n=number of things to pick from
r=number of "spots" to fill
2. Combinations are when the order doesn't matter (picking members w/o ranks, giving away identical ribbons/medals (like for participation), picking lottery numbers). If it's a combination, then you can use the "choose" formula: nCr=(n!)/[(n-r)!r!]
n=number of things to choose from
r=number of "spots" to fill
3. How can you remember what formula to use with what? Permutations get the Pick formula (PP) and Combinations get the "Choose" formula (CC).
4. A number followed by "!" doesn't mean you yell the number out loud. It means (n)(n-1)(n-2)............1.
5. 0! is equal to 1.
6. If there are N ways of doing something and M ways of doing another thing, there are NM ways of doing both.
7. To do non-distinguishable objects, use the formula (n!)/(k1!)(k2!)(k3!)..........
n=number of objects to choose from
k1, k2, k3.....=number of each non-distinguishable objects
ex) In "access" there are 2 C's and 2 S's and 6 letters in total so it's (6!)/[(2!)(2!)]
8. Circles! Basically it's (n-1)! because one person is used as a reference point and the others are arranged according to the first "thing" placed. (I think.)
9. Bracelets and Necklaces are a special circle case because you can flip them over so instead of (n-1)! it's (n-1)!/2.