So what is 3 factorial because we have 3 different things?

3 factorial over and then 3 minus 2 factorial.

So in general, we said, n choose k, that is equal to n factorial over k factorial times n minus k factorial.

Well, what's 6 choose 4?

So it's 4 s times 3 factorial over s to the fourth.

Factorial

4 times 3 times 2 times 1.

A lot of people, they learn the permutation notation and they say, oh, that's n factorial over n minus k factorial, where n is the number of things I need to place and n minus the whole thing factorial.

Times 2 times 1 s over s squared, which is we could write it as 3 factorial over what is this? s to the fourth power.

I'm sorry if that confused you when I wrote it earlier.

Factorial function using GMP

Take the elevator to the fifth floor.

He took the elevator to the 5th floor.

Well, what's going to happen?

We'll write out the words Welcome to. We'll show Steven in bold.

And of course, that and that cancel out and all you're

This will cancel with this, and so you're just left with the first 3 of 7 factorial.

I have a semi colon, and now I have a new return statement, and this is basically just the formula for factorial.

So I've loaded up this HTML into a file and you can see there is a bit of java script in the script tag here, just a simple factorial function.

We could write it as n factorial it s a lower case n n factorial over n minus k factorial.

When we did 7 things into 3 spots we went 7 times 6 times we literally put in the top three of you could almost say from the factorial.

like I showed you.

We've got this five factorial, this bang.

I think you see what I did.

So now, there's a quiz.

So is there any easy way to write that?

We're going to do the same thing with optimization.

That's 6 factorial over 4 factorial times 6 minus 4 factorial.

We proved it directly for this base case right here.

With n characters, how many ways of segmenting could there be?

Tom got on the elevator and pressed the button for the third floor.

They're 24 different ways to arrange the four blocks.

And that's just 4 s times this.

But we only took the first 3 of the factorial.

So the Laplace transform of this is equal to that.

But unfortunately, Steven is super sad.

Or another way of writing this, this would be 8 times 7 times 6 times 5 times 4 times 3 times 2 times 1 over I'll just write 3 factorial for a second.

Well, what's this?

So if I know that the Laplace transform of t the third, this is an easy one.

To write the first k of n factorial. Why sure.

The cop's chasing me.

That's 7 factorial.

Let's take that and let's divide it by that.

We have a well actually I forgot to do this should be 9 factorial.

Even though I ran down the stairs, I couldn't catch the train.