Home
Browse
Create
Search
Log in
Sign up
Upgrade to remove ads
Only $2.99/month
Math - Permutations and Combinations
STUDY
Learn
Flashcards
Write
Spell
Test
PLAY
Match
Gravity
Terms in this set (9)
What is the counting principle in maths?
When there are 'm' ways to do one thing,
and 'n' ways to do another, then there are m×n ways of doing both.
Notice how you multiply the possibilities.
Website:
https://www.mathsisfun.com/data/basic-counting-principle.html
https://www.khanacademy.org/math/statistics-probability/counting-permutations-and-combinations/modal/v/tree-diagram-to-count-outcomes
What are permutations?
A collection of things, where the order is important. Permutations refers to arrangement of things.
Example: You want to visit the homes of three friends Alex ("a"), Betty ("b") and Chandra ("c"), but haven't decided in what order. What choices do you have?
Answer: {a,b,c} {a,c,b} {b,a,c} {b,c,a} {c,a,b} {c,b,a}
When the order does not matter, such as in a fruit salad, it is a Combination.
What are combinations?
A collection of things, in which the order does not matter.
Example: For a fruit salad, how many different combinations of 2 ingredients can you make with apple, banana and cherry?
Answer: {apple, banana}, {apple, cherry} or {banana, cherry}
When the order does matter, such as a secret code, it is a Permutation.
What does the factorial operation do and what is its symbol.
The factorial operation has the symbol ! (exclamation mark) when multiplies each consecutive integer below the previous integer all the way up until 1.
E.g. 5! = 5 x 4 x 3 x 2 x 1
What is the permutation formula.
The permutation formula lets us find out the all the possible arrangements of 'n' things in 'k' spots. It gives us all the collections in all of the possible orders. Note that in permutations order matters.
nPk = n!/(n-k)!
nPk means putting 'n' things in 'k' spots considering permutations.
There is also the notation used in this video which is used more often:
https://www.youtube.com/watch?v=JVbbRCVBVRI
What is the combination formula?
The combination formula lets us find all the possible arrangements of different elements.
E.g. lets suppose we have letters ABCDE and we want to put them in 4 spots.
In the permutation world:
ABCD is not the same as ABDC
But in the combination world:
ABCD is the same as ABDC ---> however:
ABCD is not the same as ABCE.
It is just that the collection in combinations has to have at-least one different letter or 'thing'.
Formula --> nCk = n!/k!(n-k)!
Video to explain:
https://www.khanacademy.org/math/statistics-probability/counting-permutations-and-combinations/modal/v/combination-formula
What is 0!?, Explain this result.
0! = 1
This is because if you look at the formula:
nPk = n!/(n-k)!
What if k = n ---> Well then:
nPn = n!/(n-n)! = n!/0!
In order for this to be true and apply with normal permutations, 0! = 1.
E.g. we want to put 3 things in 3 spots. 3! = 3 x 2 x 1 = 6
Or 3P3 = 3!/(3-3)! = 3!/0! = 3!/1 = 3 x 2 x 1 = 6
N/A
N/A
N/A
N/A
THIS SET IS OFTEN IN FOLDERS WITH...
Math - Conic Sections - Ellipse and Hyperbola
13 terms
Math Quiz - Volume and Surface Area of Shapes - De…
12 terms
Math - Transformations
14 terms
Math - Types of Numbers
19 terms
YOU MIGHT ALSO LIKE...
Combinatorics
13 terms
Permutation
13 terms
4-6 homework
14 terms
OTHER SETS BY THIS CREATOR
Basic Computer Parts
2 terms
Module A, B and C - Study Notes
4 terms
EnglishStandard
10 terms
Metric System - Volume - Maths
5 terms
OTHER QUIZLET SETS
Mid-term review
74 terms
Quiz 3 and 4: Ch 7-11
20 terms
Intro to Psychology Final Exam Delaware State Univ…
33 terms
Basic Principles
40 terms