Permutations in probability theory and also other branches of mathematics refer come sequences the outcomes where the stimulate matters. For example, 9-6-8-4 is a permutation that a four-digit PIN due to the fact that the stimulate of numbers is crucial. Once calculating probabilities, it’s frequently necessary to calculation the number of possible permutations to recognize an event’s probability.

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In this post, I describe permutations and show how to calculation the number of permutations both with repetition and without repetition. Finally, we’ll occupational through a step-by-step example trouble that offers permutations to calculate a probability.

## Definition of Permutations compared to Combinations

Permutations and also combinations might sound favor synonyms. However, in probability theory, lock have unique definitions.

**Combinations**: The bespeak of outcomes does no matter.

**Permutations**: The order of outcomes walk matter.

For example, ~ above a pizza, you can have a combination of 3 toppings: pepperoni, ham, and also mushroom. The order doesn’t matter. Because that example, utilizing letters for the toppings, you can have PHM, PMH, HPM, and also so on. It doesn’t issue for the person who eats the pizza due to the fact that you have actually the same mix of 3 toppings. In various other words, the order of these 3 letters does no matter and they form one combination.

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Just over fifty percent of every four-digit PINs have actually repeated values.

The birthday trouble is a classic probability problem. What’s the smallest size group that has a higher than 50% opportunity of people sharing a birthday? resolving this trouble uses similar methods. Check out my post around Solving the Birthday problem to find out!