So these are all points on the different combinations between the trade offs of rabbits and berries.

Let's try some other combinations.

So we end up trying all combinations of nuts and all combinations of bolts.

These are all just linear combinations.

And these are all the combinations.

There are four combinations in total.

One can obviously also make combinations.

We're looking at all combinations of those.

You can't even talk about combinations, really.

But how can we increase the combinations?

There's nine possible combinations for A and B.

It's all of the combinations of two things.

Now why do we just call them combinations?

like middle school locker combinations, with relevant information.

And now the set of all of the combinations, scaled up combinations I can get, that's the span of these vectors.

And you say, well, how many combinations are there?

We'll learn more about that when we do combinations.

What combinations of a and b can be there?

But what's the probability of each of these combinations?

And so how many combinations are there like this?

And then how many of these combinations are there?

DNA and my wife can give 2 to the 23 combinations of DNA, then we can produce 2 to the forty sixth combinations.

It's much harder to get combinations of multiple word sequences.

Let me show you a concrete example of linear combinations.

Here I have various combinations of open and closed parentheses.

Let me write down the combinations for A and B.

The other combinations of challenge and skill become progressively less optimal.

The Mac is a demonstration of the explosive potential of combinations

So if I can give 2 to twenty third combinations of

And this was true for all the pair wise combinations of tasks.

So let me write all of the combinations that I could do.

They vary between cultures, between nations, between individuals, between social classes, between education levels.

Through evolution, winning combinations of genes, get passed on from generation to generation.

And so then you can start thinking about all of the different combinations.

Suppose we want to find words made up of combinations of musical notes.

Basically, a list of notes and modifiers and combinations over and over again.

You know, any of the unique combinations will each have the same probability.

They could take on 64 different combinations or permutations, this UAC right here.

Actually, it's overkill, because we can actually have 64 combinations here, and there are only 20 amino acids, so we can even have redundant combinations code for different amino acids.

So that's the number of unique combinations, where you have four out of six heads, times the probability of each of the combinations, which is 1 2 to the sixth power.

Amazingly, proteins are the molecules composed of combinations of only 20 type amino acids.

Now some of the greatest composers, like Bach, were combinations of these two things.

And there are a bunch of these, and we once again will use the binomial coefficient, or we'll use our knowledge of combinations to figure out how many different combinations there are.

Between

Between