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Combinations are arrangements of things that do not preserve the order. So if you have cards that say 1, 2, and 3 on them, and you want to know how many different arrangements of 2 cards you can make - you can make 3 combinations (1 and 2, 2 and 3, 1 and 3). And you can make 6 permutations, because 1 and 2 is considered different from 2 and 1.
I am begging, someone PLEASE help me figure out the difference between permutations and combinations and how to solve the problems. I have a GED book that explains it, I've watched video after video and read article after article, there is just nothing that has clicked.
"If order matters, then use permutations. If order doesn't matter, then use combinations" For many students, this "rule" causes a lot of problems. For example, consider this question: If no person is assigned more than one role, in how many different ways can a President and Treasurer be chosen from a group of 5 people? Does order matter?
Why is this permutations and not combinations ? Because Bob covering Energy, Mary covering Consumer Services, and George covering Software is different from Bob covering Consumer Services, Mary covering Software, and George covering Energy.
In permutations, the set (A, B, C) is considered to be distinct from (B, C, A) and (C, A, B). Wheras in combinations, all three are considered to be the same. So using this example of a three-element subset of a five-element set, there are 60 possible permutations, but only 10 possible combinations.
nCr= how many different combinations of people will make it to the olympics nPr= how many combinations of people can get gold, silver or bronze nCr will naturally be less. How many ways can you choose 52 out of 52 cards? 1. How many ways can you order 52 cards? 8.06+e67.
Try constructing ordered tuples and see if it changes anything. (Brazil, India, Russia) is different from (India, Brazil, Russia) because in the first case, it would imply they are pulling up to Brazil for 1 week, India for two days, and Russia for 2 weeks.
Permutations without repetition: Arranging books on a shelf. Permutations with repetition: Rolling dice or generating passwords. Combinations without repetition: Choosing a committee from a group. Combinations with repetition: Selecting flavors of ice cream when you can choose the same flavor more than once.
It helped me to learn permutations and combinations by studying a 2 x 2 table that had the formulas for the number of permutations and combinations, with and without replacement. Here's a page with a table like that. (But I note that the table appears to have an error: the number of combinations of r objects out of a set of n objects, with ...
The Combinations question is just a special case of the Subsets question, because combinations of size k, are literally just subsets of size k. Here, the order of elements chosen were irrelevant, because the combination (1,2) is same as (2,1). However the permutation (1,2) is different from (2,1).