Wednesday, May 13, 2009

It's time once more!

Looks like it's time to BOB once more! This unit has been all about the very interesting topic of combinatorics! I found this unit to be very interesting and quite a lot easier than past units. I found the entire part about combinations and permutations quite simple and straight forward. Those 2 days we spent on Pascals Triangle (or as Zhu Shijie called it, the precious mirror of the four elements) totally blew my ind just as Mr. K had promised! XD This last new part about the expansion of binomials is a little tricky still but I'm pretty sure i know what I'm doing!! So time for a review because a refresher will do me good!


When the order of a grouping of object matters with no repetition, it is called a permutation. When the order does not matter then it is called a combination.

The Fundamental Principle of Counting says that when you have N ways to do one thing and M ways to do another you have MxN ways to do both. I remember Mr. K said that this was a good way if you need a lot of suit combinations because if you have only 2 pairs of dress pants and 4 dress shirts you have 8 different suits!

We learned about factorials. A number, lets say n, factorial, symbolized by !, is written n!. This does not mean that that you shout out the letter n, it means (n)(n-1)(n-2)(n-3)......(3)(2)(1). Just incase you forgot 0!=1, that is important!!

We got a nifty little formula known as the pick formula. However Mr.k always reminds us never to rely on formulas because mathematics is the study of patterns and not crunching numbers. The pick formula if you must know is n!/(n-r)! where n is your total number of objects and r is how many ways they are to be arranged.

When dealing with non-distinguishable objects you need to divide n! by the factorial of the number of non-distinguishable objects. An example, if you did not understand that would be if you are trying to arrange the letters in book to form all possible 4 letter words. There are 4! ways to do it but because you cannot tell the 2 letter o's apart so you divide 4! by 2!.

When placing objects around a table or in a circle, the first object placed is the reference point and would not be taken into account. so for around the circular object your formula would be (n-1)!. If you have a bracelet however you need to divide your answer by 2 because you can turn your bracelet over and cut the number of possibilities in half. It is a special case. 

We also got another formula called the choose formula. It goes a little something like this. n!/(n-r)!r!. You use this when you arrange objects and order does not matter. You use this formula when the order does not matter with the objects you are arranging.

Well I believe thats all so pretest tomorrow? Or is it that we're doing another workshop to finish off the poker hands we started? Who knows!, and no, that isn't know factorial. I still may update my BOB post more so who knows. Final word of advice is that a logarithm is an exponent!! Good luck everyone!!


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