The reason this is so complicated is because of a mathematical principle called Factorials.

它之所以如此复杂，是因为阶乘这一数。

Instead of factorial time, it takes linear time.

它不是阶乘时间， 而是线性时间。

So k factorial could be written as k times k minus 1 factorial.

所以 k 阶乘以写成 k 乘以 k 减 1 阶乘。

If this was 7 over 7 minus 2 factorial we would have 7 times 6.

如果这是 7 除 7 减 2 阶乘，我们将有 7 乘以 6。

That means there are 6.24 times 10 to the 18th electrons for every negative Coulomb!

这意味着有 6。24 阶乘 每个电子 10 18 方！

So this could be rewritten as k times k minus 1 factorial.

所以这以改写为 k 乘 k 减 1 阶乘。

And here we can make a little bit of a simplification because what's k divided by k factorial?

在这里我们以稍微简化一下，因为 k 除以 k 阶乘是多少？

So we could rewrite n factorial using the same trick up here.

所以我们以在这里使用相同技巧重写 n 阶乘。

That's all this factorial stuff here.

这就是所有这些阶乘东西。

Times n minus k factorial times p to the k times 1 minus p to the n minus k.

乘以 n 减 k 阶乘 p k 乘以 1 减 p n 减 k。

So we'll take the factorial of 6 and we'll divide it by-- put a parentheses here.

所以我们将取 6 阶乘，然后将它除以 -- 在这里放一个括号。

5 factorial is 5 times 4 times 3 times 2 times 1.

5阶乘是5乘以4乘以3乘以2乘以1。

If this had 3 we would do 3 factorial, and I'll show you how that can happen.

如果它有 3，我们会做 3 个阶乘，我会告诉你这是如何发生。

That's n factorial over n minus k factorial times k factorial.

这是 n 阶乘 n 减去 k 阶乘乘以 k 阶乘。

And as you'll see it's actually 2 factorial ways that it can happen.

正如您将看，它实际上以通过两种阶乘方式发生。

And actually, it turns out that it's 2 factorial.

实际上，它是 2 阶乘。

Divided by 2 factorial times e to the minus 9 power.

除以 2 阶乘 e 负 9 方。

So if I just want 5 times 4 what I can do is I divide 5 factorial divided by 3 factorial.

因此，如果我只想要 5 乘以 4，我以将 5 阶乘除以 3 阶乘。

So times lambda to the k k over k factorial.

所以乘以 lambda k k 阶乘。

So it's a factorial of how many we're choosing from, how many shots we're taking, and the Excel function for that is fact.

所以它是我们从中选择数量、我们拍摄照片数量阶乘， 而 Excel 函数就是事实。