And if you think, this is 2 factorial.

如果你认为，这是 2 阶乘。

This is 4 factorial, 6 minus 2 is 4 factorial.

这是4阶乘，6减2是4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，我将有 7 乘 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 k 阶乘可写成 k 乘 k 减 1 阶乘。

So 6 factorial divided by 6 factorial, those cancel out.

所 6 阶乘除 6 阶乘，那些抵消了。

Once again, you'll have to know that 0 factorial is equal to 1.

再一次，你必须知道 0 的阶乘等于 1。

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

所这可改写为 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?

在这里我可稍微简化一下，因为 k 除 k 的阶乘是多少？

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

所我可在这里使用相同的技巧重写 n 阶乘。

It approximates factorials with essentially a continuous function.

它近似于具有连续函数的阶乘。

So 0 factorial divided by 10 minus 0 factorial.

所 0 阶乘除 10 减去 0 阶乘。

But 0 factorial is actually-- so that it works out properly is defined to be equal to 1.

但是 0 阶乘实际上是——所它正确地算出来被定义为等于 1。

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 n 减 k 阶乘 p 到 k 乘 1 减 p 到 n 减 k。

So 10 factorial, that's kind of the number of trials I have.

所 10 阶乘，这就是我的试验次数。

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

所我将取 6 的阶乘，然后将它除 -- 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，我会做 3 个阶乘，我会告诉你这是如何发生的。

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

5阶乘是5乘4乘3乘2乘1。

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

实际上，它是 2 的阶乘。