Videos, worksheets, games and activities to help Algebra II
students learn about permutations and combinations and how to differentiate between them
More Intermediate Algebra (Algebra II) Lessons
More Probability Lessons
Combinations and Permutations
When trying to determine the number of possible combinations in a set, it can be difficult to differentiate between combinations and permutations. With permutations, we calculate the number of possible rearrangements of a set of items. With combinations we count the number of combinations we can 'choose' from a larger set of items. Combinations and permutations are important statistical concepts.
Combinations and permutation
How to know when to use combinations or permutations.
Both combination and permutation count the ways that (r) objects can be taken from a group of (n) objects, but permutations are arrangements (sequence matters), while combinations are selections (order does not matter). For example, how many ways can you seat people at a table? That's permutation. How many poker hands are available in five-card draw? That's a combination.
How to find permutations and combinations using factorials.
1. I have 20 students in a class. I am going to pick
5 students for a prize. The first person I pick will get 1st prize, the second student 2nd prize and so on. This is called a permutation because the order matters. How many ways can I choose the students?
I have 20 students in a class. I am going to pick
5 students for a prize. They will all get the same prize. This is called a combination because the order does not matter. How many ways can I choose the students?
Permutations and Combinations
A video looking at the basic definitions of permutations and combinations.
is an ordered arrangement of r
objects chosen from n
Examples are used to show
permutation with repetition and permutation without repetition.
is an arrangement of r
objects chosen from n
objects and the order is not important.
Probability -- Combinations and Permutations: Definition of the fundamental counting principle and permutations, solving for permutation, solving for permutations with repetition, definition of combinations, solving for the number of different combination, solving for the number of different combinations of multiple events.
An example using Permutations and Combinations
In one game, a code made using different colors is created by one player (the codemaker), and the player (the codebreaker) tries to guess the code. The codemaker gives hints about whether the colors are correct and in the right position.
The possible colors are Blue,
Yellow, White, Red, Orange and Green. How many 4-color codes can be made if the colors cannot be repeated?
A club of nine people wants to choose a board of three officers: President, Vice President and Secretary. How many ways are there to choose the board from the nine people?
A card game using 36 unique cards: four suits (diamonds, hearts, clubs and spades) with cards numbered 1 to 9 in each suit. A hand is a collection of nine cards, which can be sorted however the player chooses. How many nine card hands are possible?
To win a particular lottery game, a player chooses 4 numbers from 1 to 60. Each number can only be chosen once. If all 4 numbers match the winning numbers, regardless of the order, the player wins. What is the probability that the winning numbers are: 3, 15, 46 and 49?
Quick Ways of Doing Permutations and Combinations.
You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.
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