Factorial

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

3 factorial over and then 3 minus 2 factorial.

That's 7 factorial.

Factorial function using GMP

Five factorial is 120.

It actually computes factorial.

So that's 2 factorial.

And then 2 factorial.

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

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

Well, that's just 1 factorial.

This would be 9 factorial.

So in this situation that would equal 8 factorial over 3 factorial times what?

So now 4 times 3 factorial, that's just 4 factorial over s to the fifth.

Here's one way to define factorial.

8 minus k times 5 factorial.

But we're going to have to consider 4 factorial times 5 factorial paths before we discover that.

The 3 largest components of 7 factorial.

We've got this five factorial, this bang.

So in this case, n factorial was 7.

And then what was n minus k factorial?

The exclamation mark often means factorial in mathematics.

He can't remember the value of five factorial.

It's n times the factorial of n 1.

Plus x to the fourth over 4 factorial.

The Hillis algorithm. 10 factorial gives you that number.

7 factorial will be 7 times 6 times 5.

And similarly, 6 well, 6 is also 3 factorial.

So 7 minus 3 is 4, so 4 factorial.

There's the global frame. There's our call factorial 6.

It essentially becomes 9 factorial times 2 times 1.

Things like factorial, s and tmp are all identifiers.

But all this is saying is you start doing the n factorial, but you only do the first 3 components of the factorial.

So we're just taking all the even terms. x to the eighth over 8 factorial minus x to the 10th over 10 factorial.

But we only took the first 3 of the factorial.

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

And then the numerator is the factorial of my exponent.

It's equal to 3 factorial over s to the fourth.

This expression right here is the same thing just you can relate it to the combinatorics formulas that you might be familiar with this is the same thing as 36 factorial over 36 minus 9 factorial that's what this orange part is over here divided by 9 factorial or over 9 factorial.

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.

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

left with is 8 times 7 time 6 over 3 factorial.

It would have been x to the third over 3 factorial.

This is 1 factorial over s to the 1 plus 1.