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。

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 阶乘可以写成 k 乘以 k 减 1 阶乘。

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

所以这可以改写为 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?

在这里我们可以稍微简化一下，因为 k 除以 k 的阶乘是多少？

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

所以我们可以在这里使用相同的技巧重写 n 阶乘。

That's all this factorial stuff here.

这就是所有这些阶乘的东西。

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 到 k 乘以 1 减 p 到 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 的阶乘，然后将它除以 -- 在这里放一个括号。

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的。

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。

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。

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

实际上，它是 2 的阶乘。

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

正如您将看到的，它实际上可以通过两种阶乘方式发生。

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，我可以将 5 阶乘除以 3 阶乘。

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

除以 2 阶乘 e 的负 9 次方。

So times lambda to the k k over k factorial.

所以乘以 lambda 到 k k 阶乘。

So the n minus k will become b minus a factorial.

所以 n 减去 k 将变成 b 减去一个阶乘。

This would have an N factorial complexity - that is the number of nodes, times one less, times one less than that, and so on until 1.

这将具有 N 阶乘复杂​​度 - 即节点数，减一，再减一，依此类推直到 1。

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的数量、我们拍摄的照片数量的阶乘， 而 Excel 函数就是事实。