I forget how to math

Anome

It has been over 10 years since I have taken a math class but my degree requires one so I am taking Math for Elementary School Teachers. Back when I was in elementary school, math was my best subject but that was a very long time ago. I'm working on my first assignment and most of it is going well but one question is driving me crazy. I am not trying to use this forum to cheat, the answer is in the book and this assignment isn't for marks, I just want to understand the "why" behind the answer.

a) If 8 people shake hands with one another exactly once, how many handshakes take place?

This part I got by drawing figuring out that the first person has 7 handshakes that I need to count, the second has 6, etc, coming to an answer of 28.

Generalize the solution for n people.

No idea. None whatsoever. The answer in the book is (n(n-1))/2 but even knowing the answer I can't figure out why. This is killing me inside because I know that 15 years ago this would have been easy!

Sterica

Everyone I know recommends Khan Academy to brush up on forgotten stuff like this.

DevoutlyApathetic

Anome wrote: »

It has been over 10 years since I have taken a math class but my degree requires one so I am taking Math for Elementary School Teachers. Back when I was in elementary school, math was my best subject but that was a very long time ago. I'm working on my first assignment and most of it is going well but one question is driving me crazy. I am not trying to use this forum to cheat, the answer is in the book and this assignment isn't for marks, I just want to understand the "why" behind the answer.

a) If 8 people shake hands with one another exactly once, how many handshakes take place?

This part I got by drawing figuring out that the first person has 7 handshakes that I need to count, the second has 6, etc, coming to an answer of 28.

Generalize the solution for n people.

No idea. None whatsoever. The answer in the book is (n(n-1))/2 but even knowing the answer I can't figure out why. This is killing me inside because I know that 15 years ago this would have been easy!

Khan is good stuff in general.

In this case we have 8 people who can all shake hands with 7 other people. So that can be rewritten as "We have n people who can all shake hands with n-1 people." as a general case.

But wait! Is Adam shaking hands with Bob different from Bob shaking hands with Adam? Probably not. So each handshake's order is not important so we divide the answer by the number of people in the hand shake.

The actual names for this stuff is Permutations and uses the ! symbol typically.

The Khan in question.

Savant

This is a basic combinatorics question, the quick way to get to the answer is that you are counting the number of ways to choose 2 people out of 8 (or later n) where the order doesn't matter. That gives you (8 choose 2) or (n choose 2), which simplifies to (n(n-1))/2.

Now if you don't know that ahead of time, the way to think this through is to try to figure out a way to count the number of pairings of n people where the order doesn't matter, and you can't pair someone with themselves. There are n ways to choose the first person, and since you can't shake your own hand there are n-1 ways to choose the second person, so multiply those together. But with that you will double count pairings (a, b) and (b, a) because different permutations count as the same handshake, so divide by 2. Giving (n(n-1))/2.

Ana Ng

Think of it that everyone in the group (represented by N) needs to shake hands with everyone else EXCEPT themselves, that's why you're multiplying n(n-1) and not just n*n. You are dividing by 2 because if you do not, you'll be counting everyone's handshakes twice.

To illustrate, let's say you have four people. A, B, C, D. So if you chart out all the handshake pairings you'd end up with:

AB AC AD BA BC BD CA CB CD DA DB DC

So that's 12 shakes, notice that that's the number you get if you use 4(4-1), which is your n(n-1) formula. However you'll also notice that there are repeats in there. So the first handshake is AB, but this chart also lists BA to be a second handshake, which it is not. So, if you take out all the duplicates, you are left with:

AB AC AD BC BD CD

6 handshakes, which is the result you get using n(n-1)/2: 4(4-1)/2

Is that what you were looking for? Hopefully it helped a bit, good luck with the course

Quid

As someone who could kinda sorta math but then lost all their math

If you want a book the CLEP test books are actually excellent at reteaching stuff like this. I went from the exact same situation to easily passing the college algebra test. I'd recommend looking in to one of those for something physical.

davidsdurions

Now, I'm not sure if this particular topic is in this book, but I know the next book Forgotten Calculus was amazing for helping me brush up on calc stuff so I'm going to assume this one would be excellent for everything trig and prior. For $4, it's difficult to go wrong.

Also khan academy yes. The app is great if you just need the videos and the website is pretty slick for practicing the maths.

Lastly, are they really teaching this stuff to elementary students these days? If so, I was robbed with my public school education.

Anome

Savant wrote: »

This is a basic combinatorics question, the quick way to get to the answer is that you are counting the number of ways to choose 2 people out of 8 (or later n) where the order doesn't matter. That gives you (8 choose 2) or (n choose 2), which simplifies to (n(n-1))/2.

Now if you don't know that ahead of time, the way to think this through is to try to figure out a way to count the number of pairings of n people where the order doesn't matter, and you can't pair someone with themselves. There are n ways to choose the first person, and since you can't shake your own hand there are n-1 ways to choose the second person, so multiply those together. But with that you will double count pairings (a, b) and (b, a) because different permutations count as the same handshake, so divide by 2. Giving (n(n-1))/2.

This helps a lot, thank you. I'll be sure to check out Kahn Academy as well.

Thanks everyone, I think I've got this.

Nija

I took a statistics class over the summer and this is another vote for Khan Academy. The videos are excellent and the learning curve of the software is good. However, don't do what I did, and start remembering the answers. It is counter-productive to the exercise and doesn't help you when you need to actually work out the problem.

I think I logged 15 hours on Khan Academy (over the 6 weeks of the course). I ended up getting an A. The first A in a math class, ever. Khan wasn't all of it, but I felt it gave me enough of a boost, that it was appreciated.