How do I use permutations and combinations?

Permutations are used when the order matters in arranging items. Combinations used when the order doesn’t matter in choosing items. Permutations calculate all possible arrangements, while combinations count only the unique selections.

Permutations: Use when order matters (e.g., arranging seats) Combinations: Use when order doesn’t matter (e.g., choosing team members)

The two techniques are used to solve real-world problems by determining the number of ways that are useful to arrange and select objets. This can be done without listing all objects. For example, anagrams could be used to arrange objects.

Permutations and combinations are ways to count possible selections or arrangements from a set of items, but the difference lies in whether the order matters. Permutations: Used when the order matters. Combinations: Used when the order doesn’t matter.

They are used when data is to be arranged in a number of ways.

Permutation and combination are used to solve real-world problems by determining the number of ways that are useful to arrange and select objets. This can be done without listing all objects.Permutations: Used when the order matters. Combinations: Used when the order doesn’t matter.

Permutation are used where order matters and combinations are used where order does jot matter.both are used to count possible outcomes from a set of objects difference is only for order

Yes they have real life applications as to seek possible selection or arrangements from a set of objects by doing quick calculations

Hi, those are used to count the number of possibilities in probability problems. 5 people running a race there 5P5 possible outcomes, 5*4*3*2*1=120. Combinations are used when order is NOT important.

Permutations: Permutations refer to the number of ways in which a set of elements can be arranged or ordered. The formula for calculating permutations is: P(n, r) = n! / (n-r)! Where: - n is the total number of elements - r is the number of elements being arranged - ! represents the factorial operation For example, if you have 4 books and you want to know how many ways you can arrange them on a shelf, the number of permutations would be: P(4, 4) = 4! / (4-4)! = 4! / 0! = 24 Combinations: Combinations refer to the number of ways in which a set of elements can be chosen, without regard to the order of selection. The formula for calculating combinations is: C(n, r) = n! / (r! * (n-r)!) Where: - n is the total number of elements - r is the number of elements being chosen - ! represents the factorial operation For example, if you have 5 books and you want to know how many ways you can choose 3 of them, the number of combinations would be: C(5, 3) = 5! / (3! * (5-3)!) = 5! / (3! * 2!) = 10 Finding factorial : 1! =1 (1*1) 2!=2 (1*2) 3!=6 (1*2*3)

Eg. Permutation (Arranging people in a line) Combination (Choosing a team)

Dear Alice, permutations are used when the question mentions that the order of choices you make matters. Combinations mean the order does not matter. For example, if you are forming a group it does not matter who you pick first and then second, but when you want to rank them from best to worst order matters.

Used when the arrangement of objects is important. Formula: 𝑃 ( 𝑛 , 𝑟 ) = 𝑛 ! ( 𝑛 − 𝑟 ) ! P(n,r)= (n−r)! n! ​ Where: 𝑛 n = total number of objects 𝑟 r = number of objects to arrange ! ! = factorial (e.g., 5 ! = 5 × 4 × 3 × 2 × 1 5!=5×4×3×2×1) Example: How many ways can you arrange 3 books from a set of 5? 𝑃 ( 5 , 3 ) = 5 ! ( 5 − 3 ) ! = 5 × 4 × 3 ! 3 ! = 5 × 4 = 20 P(5,3)= (5−3)! 5! ​ = 3! 5×4×3! ​ =5×4=20 Combinations (Order doesn’t matter): Used when the selection of objects is important, but the order doesn’t matter. Formula: 𝐶 ( 𝑛 , 𝑟 ) = 𝑛 ! 𝑟 ! ( 𝑛 − 𝑟 ) ! C(n,r)= r!(n−r)! n! ​ Where: 𝑛 n = total number of objects 𝑟 r = number of objects to choose

Permutations are used when order matters, while combinations are used when order doesn't matter.

Permutation applies when order in involved in arrangements and combination doesn't tell us order in arrangement

The two techniques are used to solve real-world problems by determining the number of ways that are useful to arrange and select objets. This can be done without listing all objects.

permutation and combination are concept which we apply when we need to find in how many different ways can a task be done if we have n objects and we need to give r of them to r children we use combination to select r objects from n and give them to children but if we make a queue of those r object we use permutation because for same 2 objects queue can change by interchanging there position for 3 objects A,B,C permutations can be ABC,ACB,BAC,BCA,CAB,CBA but there will be only 1 combination we just need to select 3 objects from A,B,C

*Permutations* - Order matters (e.g., arranging items in a specific sequence) - Formula: nPr = n! / (n-r)! - Where: - n = total number of items - r = number of items being chosen - ! = factorial (e.g., 5! = 5 × 4 × 3 × 2 × 1) Example: Arrange 5 people in a line. n = 5, r = 5 5P5= 5! / (5-5)! = 5! = 120 Note: 0!=1 *Combinations* - Order doesn't matter (e.g., selecting items without regard to sequence) - Formula: nCr = n! / (r!(n-r)!) - Where: - n = total number of items - r = number of items being chosen - ! = factorial Example: Choose 3 fruits from 5. n = 5, r = 3 5C3 = 5! / (3!(5-3)!) = 10 Key differences: - Permutations: Order matters, use nPr - Combinations: Order doesn't matter, use nCr Common applications: - Permutations: Scheduling, arranging objects, password generation - Combinations: Team selection, lottery, committee formation Do you have any specific questions I can help you with? Send me a message.

Permutations and combinations are used to define arrangements the difference is in combinations order don't matter but in combinations order to. For example if you have four objects A B C D the ways to arrange them differently would be 4! Which is 24. Also if you want to choose the different ways 2 out of those 4 objects can be arranged where order doesn't matter then you do 4C2 which would be 6 meaning it could be AB AC AD BC BD CD and if order does matter then it would be 4P2

* Permutations are used when order/sequence of - arrangement is needed. * Combinations are used when only the number of possible groups are to be found, and the order/sequence of arrangements is not needed. Permutations are used for things of a different kind.

An example of permutation is when I have a group of objects, and I want to find how many ways I can arrange the objects. The combination gives me the number of combinations the of the object and the order does not matter.