Now we get to a very exciting topic and that's called combinations. The first time you meet combinations you're going to be quite amazed by them. Now, we've all played this little game at school Imagine we have ten children on the playing field outside. We've got two captains and they've got to make two teams of five. So they've got to choose five from that set of ten. And let's just play this game a little bit differently. We let one of the captains decide first. He or she can go first and from those ten children, he or she can pick five. You've got to ask yourself, how many different teams can that captain come up with And the answer might amaze you. Remember, only ten children, you just have to pick five of them, how many different teams can be made? And there you see the answer. >252 different teams just from choosing five individuals from a group of 10. That's actually quite amazing. That amazes me now, 253, that's a bit difficult to explain. So, let's just go a little bit lower in our numbers. Let's have four colours. We're going to have red, green, blue and yellow. And we're just going to say, from those four, let's make groups of two. How many groups of two can be made from these four colours? Well it's quite easy. There's six combinations that we can make. It's really gonna be the red/green, the red/blue, the red/yellow, the green/blue, the green/yellow, and the blue/yellow. It's easy to do. Now for something more exciting than the colours, let's play the lottery. This is actually important because some of us spend our money on the lottery. Now in most countries you have to pick six numbers and you pick from a possible of say, let's make in our example you have numbers one to 47. So there's only 47 numbers to choose from. And you've gotta pick six. How many different combinations of 6 can be made from a possible pool of 47 numbers? And again, we know it's very unlikely to win the lottery, so you can imagine the number's quite large. But it might amaze you to find out that there's more than ten million different combinations, >10,737,573. That's enormous and that's why you don't win the lottery. Because if you picked six numbers that's one in >10 737 573. So I worked it out for you there. What your probabilities, your likelihood of winning the lottery is, actually very small no wonder they say playing the lottery is just another form of tax for people who don't understand mathematics. And all fun and games apart this, I mean, serious hidden behind combinations. And something that you have to understand in order for you to understand the and statistics that we are dealing with. Now we just aw that we had 47 individuals and we had to choose six from that. We could make groups of six and that gave us over 10 million different combinations. And that's quite amazing but now think about it in different terms imagine you were to do a study and there are 47 and six those two numbers involved. So what can we do? Let's imagine instead of seven billion of us on the face of the earth. There are only 47 people and you want to do a study, and in your study you want to include six individuals. So from that 47 people you're going to take six. You're going to measure some variables so their white cell count whatever and you're going to calculate a mean. And you might make two groups and compare those means but how many groups could you have come up with? Just 47 people just groups of six. Over ten million. You would have been able to calculate more than ten million separate different means. And that's just from 47 people. So imagine we ramp that up to seven billion people and you included in your study just 30. That mean that you can work out for whatever variable, is just one of almost a countless number of other means you could have come up with. And that lies at the heart of the central limit theorem which we'll get to next.