Thursday, May 7, 2009

Permutation and Combination

Hi guys, I'm here to scribe for today. We learn about the difference between Permutations and Combinations.



Permutations
: If the order does matter.


Combinations: If the order doesn't matter.

Permutation and Combination is a bit confusing topic. "Click this" if your confused a little bit about this topic. I hope it will help you.


this are the topics we discuss today:



I.


We have 4 couples in the table. It means that there are 8 people in the table. Sometimes it might be confusing.

a) First we set a reference point in the circle. Then in the opposite of the reference point was his/her spouse. So in the other side there is only 1 arrangement that is possible. Besides the reference point there are 6 possible choices who can sit in that chair and in the opposite side was his/her spouse. There is no other people except the spouse who can sit in that chair because of some restriction given. Next chair was 4 possible choices because there are only 4 people left (da!!). And so on....Multiplying those number of possible outcomes will result to the answer which is 48.
b) In this case men and women must be seated alternate. We assume that the ladies will sit first so we set a reference point. The number of possible outcomes will be 3!(three factorial). Then 4!(four factorial) for the gentlemen. Multiply the possibilities and it will lead to the answer which is 144. Remember, in circular table it doesn't matter if the ladies will sit first or the gentlemen because if you rotate it you can't identify which is first(does it make sense?).






II.
Necklace can be flip so there is duplication. To avoid that we divide the number of possibilities that will occur and remove the duplication by dividing by 2.





III.

Consider "mom" and "dad" as 1 and set them as a reference point. 3!(3 factorial) is the possible arrangement for the boys and 3! also for the girls. And for the parents are 2!. If this numbers were multiplied the number of outcomes will be 72. In the other hand we can solve it in different way as drawn above. "M" stands for the name of the mother and "J" stands for the name of the father.




IV.



In this problem order doesn't matter. It can be solve by choosing letters that can be made with those letters. Y is for yes and it means that the person is chosen as part of the committee and N for no. So there are 7 letters consist of 3 Y's and 4 N's. 7! over the number of repeated letters will let you show the answer. the real answer is 35.
It can also be solve by "Choosing" 3 people out of 7 (
7C3).






V.




For further questions and correction leave a comment. I'm so sorry if my grammar is still awful. To be honest I'm not good in English and I'm still learning it. Apologize to all of you guys. And also for late scribe.

Next scribe is aldrin
YEY!

1 comment:

  1. as pj stated, you just label it combinatorics.

    ReplyDelete