How many different ways can objects be organized? Learn how to describe and calculate permutations in this video.
- [Instructor] Probabilities are ratios, a desired event divided by all the possible outcomes. For example, the probability of drawing an ace from a standard deck of 52 cards. Desired event; draw one of the four aces possible. Possible outcomes; 52 cards. Easy, we know there are four aces, we know there are 52 cards. But when you're out there all alone in the real world, sometimes isn't that easy to figure out what all the possible outcomes are. That's why it might be helpful to understand permutations and combinations. Both attempt to give us every possible outcome. The difference is that permutations are interested in the order of things and combinations are not. In this video, I'll cover permutations. For example, the letters A and B can be arranged in two permutations, AB, and BA. How about the numbers, 1, 2, 3? Here we have six permutations. But as the number of objects increases, listing them out becomes more difficult. Let's try this problem. Five people enter into a competition. They will be judged first through fifth. What are all the different ways these five people might end up ranked? To find the number of permutations of these five contestants, we use this simple formula. We call this N!. What does that mean? It simply means that if we have five objects, we calculate five!. Which means we multiply 5 x 4 x 3 x 2 x 1. Yep, believe it or not, there are 120 different ways in which these five contestants can finish this contest. How about if we had six contestants? 720 different permutations. Let's take a different example. Let's say there's a race with 8 runners. Prizes will be awarded to only the top three finishers. How many permutations are there for only the top three spots, when you have 8 contestants? Here we use a different formula, N! divided by the quantity N minus X!, where N is the total number of objects. In this case, that would be our 8 runners. And X is the number of objects to be selected, in this case, we are interested in the top three finishers. So it's 8! divided by 8 minus 3!. We end up with 8! divided by 5!. Notice we have 5, 4, 3, 2 and 1 on both the top and the bottom, so we can cancel those out. So we end up with 8 x 7 x 6, 336 different permutations for those top three spots when we have 8 runners. So as you consider things like general probability, rankings, seating arrangements or scheduling, or as you ponder just how many possible outcomes might there be for a certain situation, consider utilizing the basic permutation formula to better understand a situation.
Eddie explains that probability is used to make decisions about future outcomes and to understand past outcomes. He covers permutations, combinations, and percentiles, and goes into how to describe and calculate them. Eddie introduces multiple event probabilities and discusses when to add and subtract probabilities. He describes probability trees, Bayes’ Theorem, binomials, and so much more. You can learn to understand your data, prove theories, and save valuable resources—all by understanding the numbers.