组合 - 概念

Now we're going to look at the number of different ways to select 3 students from a class of 20. And what I see is that we're trying to select 3 kids and it doesnÂ’t say anything about the order we're choosing them, so no matter what 3 kids we chose it's always going to be the same. So if we chose student a, b and c it's the same exact selection as if we chose c, b, a okay it's just the final 3. Which tells me we're going to be doing a choosing operation, basically all we do is the number of students in the entire class. 20 choose the number of students that we are concerned with which is just going to be 3 okay. I do want to talk about another we could actually write this question, this turns into being 20 factorial over 20 minus 3 factorial, 17 factorial times 3 factorial.
The other we could actually do this is say you're choosing these students that you donÂ’t want to select okay and so if we said 20 choose 17 we actually get the exact same answer what this turns into is 20 factorial divided by 20 minus 17 factorial is 3 factorial over 17 factorial. So a choosing order doesnÂ’t matter quite as much because basically if you choose the people you want or you choose the people you dnÂ’t want you're going to end up with the exact same thing okay.
通常，你要只是为了看起来更容易说好，也可以选择你正在处理的号码，但是关于选择的幸运是，如果你这样做，你仍然是正确的答案。