The Permutation Formula and Why it Works | Permutations and Combinations, Counting, Combinatorics

What is the permutation formula and why does it work? The permutation formula tells us how many ways r objects can be ordered from a collection of n objects. We'll be going over this formula in detail in today's math video lesson! Including several permutation example problems!

The permutation formula uses factorials. Remember, for example, that 5 factorial is written as 5! and is equal to 5*4*3*2*1. Similarly, 7! = 7*6*5*4*3*2*1.

One important thing about the permutation formula is that it assumes objects cannot be repeated. And always remember that with permutations order is important. A permutation is an ordering of a collection of objects, so the number of permutations is the number of ways some objects can be ordered! We'll go over all of this in detail in the full lesson!

SOLUTIONS TO PRACTICE PROBLEMS:

First let's tackle the problem that does not allow repetition. How many objects are we ordering? The code is 5 digits, so we are ordering 5 objects. How many objects can we choose from? We can choose from the digits 0 through 9, which is a total of 10 choices. Thus, using our formula, the number of 5-digit codes that can be created from the digits 0-9, without repetition of digits, is P(10, 5) = (10!) / (10 - 5)! = 10!/5! = 10*9*8*7*6 = 30240.

What if repetition of digits is allowed? Then for the first digit of our code we have 10 choices, for the second digit of our code we have 10 choices, for the third, fourth, and fifth digits we also have 10 choices. Thus there are 10*10*10*10*10 = 10^5 total 5-digit codes possible in this scenario.


I hope you find this video helpful, and be sure to ask any questions
down in the comments!

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