That's 4 factorial over 2 factorial times 2 factorial, right?

So 4 factorial divided by 0 factorial times 4 factorial.

That's equal to 10 factorial over 2 factorial times 8 factorial.

It's 4 factorial over 2 factorial times 4 minus 2 factorial.

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

That's 4 factorial over 3 factorial.

This means 10 factorial over 2 factorial times 10 minus 2 factorial.

So you get 4 factorial over factorial.

So that's 4 factorial over 3 factorial.

So this is equal to 4 factorial over 0 factorial times 4 factorial, right 4 minus 0 is 4 a to the fourth plus 4 factorial over 1 factorial times 3 factorial, right?

That's plus 4 factorial over 4 factorial times 0 factorial b to the fourth.

Factorial

4 minus 2 factorial, that's also 2 factorial.

10 factorial divided by 9 factorial that's 10.

3 factorial over and then 3 minus 2 factorial.

So that's 4 factorial over 1 factorial, which is also 1, divided by 4 minus 1 factorial.

4 factorial.

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

That equals n factorial over 1 factorial divided by n minus 1 factorial times x to the n minus 1.

That's equal to 4 factorial over 0 factorial, which, you may or may not know, is defined to be 1, over 0 factorial divided by 4 minus 0 factorial.

That's 7 factorial.

That's 26 factorial.

If I have 7 factorial divided by 6 factorial, that's just 1.

With just the 1 factorial and the 3 factorial got switched around.

Five factorial is 120.

1 factorial is 1.

Five factorial is 120.

Over what's 2 factorial?

So n factorial divided by n minus 1 factorial, that's just equal to n.

You shouldn't just memorize it. n choose k from our combinatorics is equal to n factorial over k factorial divided by n minus k factorial.

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

This would be 9 factorial.

So the 8 factorial, if you divide into 10 factorial, that's going to cancel out with that.

10 factorial gives you that number.

4a cubed b plus 4 factorial.

Or if I have 3 factorial divided by 2 factorial, that's just 3, you can work it out.

The 3 largest components of 7 factorial.

To write the first k of n factorial.

So in this case, n factorial was 7.

And then what was n minus k factorial?

And we're going to divide by 6 factorial.

4 minus 3 is 1 factorial. ab cubed.

So it's equal to 4 times 3 times 2 times 1 divided by 2 factorial is 2 and 2 factorial is 2.

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

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.