# Permutations in Statistics

**A free video tutorial from**Vijay Gadhave

Data Scientist and Software Developer

4.3 instructor rating •
8 courses •
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### Learn more from the full course

Statistics Masterclass for Data Science and Data AnalyticsBuild a Solid Foundation of Statistics for Data Science, Learn Probability, Distributions, Hypothesis Testing, and More!

05:08:47 of on-demand video • Updated August 2020

- Understand the Fundamentals of Statistics
- Understand the Probability for Data Analysis
- Learn how to work with Different Types of Data
- Different Types of Distributions
- Apply Statistical Methods and Hypothesis Testing to Business Problems
- Understand all the concepts of Statistics for Data Science and Analytics
- Working of Regression Analysis
- Implement one way and two way ANOVA
- Chi-Square Analysis
- Central Limit Theorem

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Hello beautiful people there and welcome to the statistics tutorial in this tutorial we will learn permutations. Let us begin in the statistics permutation is the act of arranging objects in both equations. Let us understand this with the help of an example. We how to calculate all the possible permutations four letters A B and C there are six possible permutations four letters a b and c d are as follows A B C ACB b aC B C A C A B and C B A. We can calculate number of permutations with the help of a formula. Also let us see how for the letters abc we can calculate the number of possible permutations as N Factorial. There are three letters in ABC means three factorial three factorial is calculated as three to two into one. Haines Vale six permutations. So this way we can calculate simple permutations let us understand how can we calculate permutations for a subset. The number of permutations for an object and taken out objects at the time from N is given by following formula n factorial divided by n minus out of factorial here and is the total number of objects and add is the number of objects that is taken from an let us understand permutations for a subset. With the help of an example a website requires to create a password of four characters. These characters can be law guess letters or digits from 0 to 9. Here we have one more condition. We cannot repeat the letters or numbers. So how many different passwords can be created. To solve this question first we are to calculate total number of objects that is and there are 26 letters and 10 digits Heinz and is equal to 36 then we are able to calculate are number of objects taken at a time are is equal to four and at the end we to apply formula 36 factorial divided by thirty six minus four factorial calculation is very simple 36 factorial can be written as 36 in 235 in 234 up to 1 and 32 factorial can be written as 32 in 231 in 230 up to when after the calculation Valdis result 14 like thirteen thousand seven twenty permutations. So this is how we can calculate departure mutations for a subset. Here we have the same question that we have seen earlier. A website requires to create a password of four characters and these four characters can be lower case letters or digits from 0 to 9. But here we can repeat the letters are numbers. So how many different passwords can be created the number of arrangements of an object taken are objects at a time the reputation can be calculated by this formula. And these two are in this question total number of objects are 36 and taken objects have for Heinz 36 is two fold. So we can create this number of passwords when we allow repetition of the characters so friends the statistics tutorial ends here. Let us revise what we have learned in this tutorial. First we understood that we can calculate total number of permutations offset and by this formula and factorial. Then we understood how to calculate permutations for an object when our objects are taken. We have understood this with two conditions with no reputation and with reputation I will see you in the next statistics tutorial build and enjoy learning statistics.