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Permutations

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Permutations

Study Guide

Key Definition

A permutation of a set is an arrangement of its members into a sequence or order. The number of permutations of $n$ objects is $n!$.

Important Notes

The formula for permutations of $n$ objects taken $m$ at a time is $P(n, m) = \frac{n!}{(n-m)!}$.
In permutations, order matters.
Factorial of a number $n$ is the product of all positive integers less than or equal to $n$.
Commonly used in arrangements where the sequence is important.
Different from combinations where order does not matter.

Mathematical Notation

$n!$ means factorial of $n$

$P(n, m)$ represents permutations of $n$ objects taken $m$ at a time

Remember to use proper notation when solving problems

Why It Works

Permutations calculate the number of ways to arrange a set of items where the order is important. This uses factorial mathematics to determine the total possible arrangements.

Remember

Permutations are used when the order of arrangement is important, such as in scheduling or ordering tasks.

Quick Reference

Permutation Formula:$P(n, m) = \frac{n!}{(n-m)!}$

Understanding Permutations

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Permutations allow us to count the arrangements of items where order matters, using the formula $n!$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

How many ways can you arrange 3 books on a shelf using the permutation formula $n!$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You have 5 different video games and 3 available slots in your game console. How many different ways can you arrange the games to play?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

A school dance committee needs to arrange 4 songs in a specific order from a list of 7. How many different playlists are possible?

Challenge Quiz

Single Choice Quiz

Advanced

How many ways can 10 different books be arranged on a shelf, if 4 are to be selected?

Recap

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Review key concepts and takeaways