Permutations and Combinations
Everything Everywhere Daily: History, Science, Geography & More
Gary Arndt
4.7 • 2.3K Ratings
🗓️ 2 August 2023
⏱️ 15 minutes
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| 0:00.0 | Whenever there is a lottery, the odds of winning are given. |
| 0:03.0 | If you go to a pizzeria, they may tell you the number of possible pizzas that can be made given their toppings. |
| 0:08.0 | If you have a combination lock, it's secured because of the number of different solutions that are possible. |
| 0:13.7 | All of these things might seem different, but they're all part of the same branch of mathematics. |
| 0:18.6 | Learn more about permutations and combinations and how they work on this episode of Everything Everywhere Daily. If you're not familiar with permutations and combinations, do not fear. |
| 0:44.0 | It's a subject that often isn't covered in basic mathematics courses, but it also isn't that complicated. |
| 0:50.0 | It involves nothing more than basic multiplication and division. It doesn't necessarily even involve fractions or decimals, just whole numbers, and |
| 0:58.0 | they can usually be explained using everyday things that you are familiar with. |
| 1:02.4 | So to start this discussion discussion let's take a very |
| 1:04.7 | simple case. How many ways can you arrange the numbers one, two, and three? This is a |
| 1:11.1 | pretty small number of things so we could just brute force this and write them all out. |
| 1:16.0 | There are one two three one three two one three two one three three one two and three two one. 231, 3.12, and 321. |
| 1:24.0 | So there are six ways you can arrange the numbers 1, 2, and 3. |
| 1:29.0 | Now let's say we want it to do the same thing with one, two, three, and four. Well that suddenly |
| 1:35.1 | becomes much harder. Not ridiculously hard, but hard enough that you don't want to |
| 1:39.6 | listen to me read out strings of numbers for the better part of a minute. |
| 1:42.4 | Is there a way we could make a |
| 1:44.7 | simple formula for calculating this? Well, there is. Let's say I have balls numbered |
| 1:50.4 | one, two, three, and four in Hopper, and I pull them out to create an arrangement. |
| 1:55.2 | For the first ball, there are four possibilities because all four balls are still in the hopper. |
| 2:00.8 | Once I pull that ball out, there are now three possible balls that I could select. |
| 2:05.0 | Once I pull that ball out, there are now two possible balls left, and then finally, there is only one ball left. |
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