![]() ![]() So basically choosing order doesn't matter, permutation order does pick a way to remember that and stick with it up till now I don't really have any good sort of memory devices but hopefully you can come up with one. The numbers are exactly the same so this is still 10 and 3 but instead of choosing we end up using a permutation okay. So this one the different ways are that a medal is a permutation. ![]() So if we switch the first and the third person we're going to get a completely different permutation, we've switched the gold and the bronze we're going to get a completely different result. The difference with that and permutation is that with permutation order matters. And in this case we're dealing with 10 people so this is just going to be 10 choose 3. So this is going to be a choose, order doesn't matter first and third can switch is the same combination of everything. Okay so we said that order doesn't matter for choosing okay so order doesn't matter means that we are dealing with this sort of general grouping okay. So if the gold and the bronze person switch places they're still the same combination on that medal stand. The other one is how many different groupings could there be on the medal stand? So basically there you have a trio of people no matter what that trio is, it's going to be the same. So we have a running race there're 10 people on it and there's 2 things we're concerned with, the first is how many different ways are there to medal? So that takes into account gold, silver, bronze or otherwise first second, third place. So what I want to do, is just do a fairly simple example and start to distinguish the difference between the 2. So either way you think of it as long as you know that order matters for a permutation you're okay. Either way permutation is going to be a line order matters, combination is going to be a bag order doesn't okay. So you're sort of dealing with a linear versus the bag or order matters versus it doesn't. Whereas combinations are sort of just a collection of objects so you put a bunch of things into a bag and the order in that bag doesn't really matter. ![]() You go first, second, third, fourth, fifth so on and so forth, so you sort of place them in a spot. So permutation order matters, combination order doesn't okay.Īnother way you can think of it is permutation is a way that things are organized sort of in a linear fashion. A combination will not, you choose 2 things, it doesn't matter what the order is going to be. So in general the sort of rule of thumb that I use is that with permutations order matters okay and so what I mean by that is you pick one thing you pick another, a permutation is going to allow a different result if you switch the order of those 2 okay. They're both distinguishing you know you have a certain number of things and you're taking a certain number from that but how we know when to use each can be a source of confusion. Well common problem that students have is to distinguish the difference between permutations and combinations. ![]()
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