Permutations Combinations and Anagrams

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Permutations Combinations and Anagrams

by bpolley00 » Thu Dec 27, 2012 7:08 pm
Hey everyone, so far I have really struggled with Permutations, Combinations and Anagrams. Thus, I was hoping to get a forum post that was completely devoted to not only answering these questions but also doing so efficiently. In addition, I was hoping to be able to get an explanation on distinguishing these types of questions on the test. So my goal for this post is to go over what I have as far as study materials and to see if I cannot get Ron or some other expert to verify/ elaborate further, in a more concise manner.

Anagrams- These questions are usually asking for arrangements. So for example, how many arrangements of 6 books on a shelf can you make? The answer is merely 6! = 720. If you have a question that asks how many combinations of Pizzazzz can you make it would be 8!( Total number of letters)/ 5! (repeated Letters) =8*6*7=336. Another Example would be Atlanta= 7!/3!2! Which I will let you guys figure out.

Coin Flip Questions- Get K Flips out of N Flips. So what is probability that you get 3 heads out of 4 flips? The equation I have is NCK/2^n Where NCK= N!/k!(N-K)! So for this question you would have NCK= 4!/3!1!= 4 4/ 2^4= 4/16 = 1/4

Combinations- are known as unordered subgroups where basically order doesn't matter. Thus, I merely have the NCK equation So N!/K!(N-K)! Which is very similar to the coin flip.

Hard Question: A Volcano has a 50% probability in a year to erupt. What is the probability that it erupts 2 years in a 5 year period? The only way i know to solve this is with the Binomial Distribution Formula = NCK*p^k * (1-p)^(n-K)

I watched the Thursday with Ron on the Slot Method; However, I didn't really quite get it with the order does matter vs order doesn't matter.

Basically, I just need a summation of someone who is getting 100% of these questions correct to give me an explanation of exactly what approach you are taking per different questions and how you are distinguishing which approach to use, as I feel that my approach is quite formula heavy and not very intuitive.

Thanks so much for taking the time to read my post guys and I look forward to hearing your responses.

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by MartyMurray » Fri Nov 21, 2014 1:34 pm
To make it all more intuitive, one thing I do is just look at what's going on and, in a way anyway, create a formula myself. Yes, I already know most of the formulas I am going use. At the same time, the foundation of what I am doing is not so much memorizing formulas as understanding concepts.

For instance, in your books on a shelf example, I have the basic idea, and without memorizing a formula I realize that I can choose from six books to put in the first slot on the shelf. That starts the arrangement six different ways.

Then for the next slot there are five choices left. So I started six ways and for each of those six ways I have five choices for the next slot. Already we have 6 x 5 = 30 different arrangements.

This goes on for the next four slots, and for each there are fewer books to choose from, and I end up doing just what you said, 6! = 6 x 5 x 4 x 3 x 2 x 1, except I didn't exactly memorize a formula. Rather I knew how it worked in reality, and applied that to basically create the 6!.

Now if there is some twist in how the arrangement is to be made, maybe a certain book has to be first, I just change my math to fit that twist and create a formula or set of formulas that will get me to the answer.

That's the general idea with these questions. There is a logic to how they get answered, and rather than just memorizing formulas, you can apply that logic to quickly come up with a formula that fits a particular situation.

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by 009hnoor » Wed Apr 29, 2015 1:08 am
Then for the next slot there are five choices left. So I started six ways and for each of those six ways I have five choices for the next slot. Already we have 6 x 5 = 30 different arrangements.