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

它之所以如此复杂，因为这一数学原理。

Instead of factorial time, it takes linear time.

它时间， 而线性时间。

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

所以 k 以写成 k 以 k 减 1 。

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

如果这 7 除 7 减 2 ，我们将有 7 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 每个电子的 10 到 18 次方！

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

所以这以改写为 k k 减 1 。

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 的多少？

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

所以我们以在这里使用相同的技巧重写 n 。

That's all this factorial stuff here.

这就所有这些的东西。

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

以 n 减 k p 到 k 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，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.

55以4以3以2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，我会告诉你这如何发生的。

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

这 n n 减去 k 以 k 。

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

正如您将看到的，它实际上以通过两种方式发生。

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

实际上，它 2 的。

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

除以 2 e 的负 9 次方。

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 以 4，我以将 5 除以 3 。

So times lambda to the k k over k factorial.

所以以 lambda 到 k k 。

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.

所以它我们从中选择的数量、我们拍摄的照片数量的， 而 Excel 函数就事实。