11/29/2023 0 Comments Permutation or combinationThat's number 1 followed by number 9, followed by number 7, followed by number 7. With Permutations, you focus on lists of elements where their order matters.įor example, I was born in 1977. The key difference between these two concepts is ordering. I'm going to introduce you to these two concepts side-by-side, so you can see how useful they are. Additionally, now we cannot repeat an arrangement of digits if they ALL are the same digits.Permutations and Combinations are super useful in so many applications – from Computer Programming to Probability Theory to Genetics. The first constraint is that we cannot replace or re-use a digit once it is used (same as permutation above). Here, we start off with 3 total digits that we can use. NO replacement.įind 2-digit code with NO replacement AND with repetition. Now let's assume that we have the same lock with 2-digit code, however now if a digit is used once in the 2-digit-code, then it cannot be used again i.e. Thus the possibilities of arranging the code could be anything. Combination: NO replacement AND NO repetition (or rearrangement of the same set)Ĭode to a lock with 2-digits: - using only three digits: 7,8 and 9įind all possible 2-digit codes for the lockīecause here we assume that our lock could have "replacement and repetition".Permutation: NO replacement AND repetition (or rearrangement of the same set) allowed.Lock: All combinations allowed (with replacement AND repetition both).$ or $$ does not matter, we can pick only one of those two arrangements.] 'Does not matter' actually means 'no replacement' AND 'no repetition within arrangement' Thank you for question and explanations above. You need to divide it by 3! because there will be Clearly you cannot just divide the permutation by 3 to get 4060. If you are choosing 3 people it gets worse becauseģ0P3 = 24 360 but $30\choose3$ is 4 060. Why is that? Obviously because for every Fred and Eddie there was a Fred Eddie) Note that 870 is double 435 so see how in this case you would have had 870 full arrangements but only half of them are valid choices. This is one where order doesn't matter because picking Eddie and Fred is the same as Fred and Eddie How many ways can you choose those people. If there are 30 people in a class and you need to pick 2 people to clean up at the end of the day. A permutation is all the ways of arranging all the combinations into specific orders like in a) You can't say a lock has 10P3 = 10 x 9 x 8Ī lock has different numbers for each positionĬ) The combination is just the number of choices provided we are not ordering the items but choosing a certain amount of them and grouping them together. Locks don't have permutations or combinations actually Finding all the arrangements would includeīut the same three people were in there so if order didn't matter, this would only count as 1 arrangement since in each case there was 1A, 1B, 1C.ī) You're right that's clever. Say you have 3 people (A, B, C) and you want to put them in a row. Thank you!Ī) this one depends on the question at hand. I look at another and have no idea how to do it! I'd greatly appreciate any help. I'm really struggling with this and every time I think I understand a scenario/problem. then why are the number of permutations larger than the number of combinations? Therefore it seems like order does matter.Ĭ.) If permutations are ALL ways of doing something and if EVERY detail matters. why are "Locks" said to have a "combination" when clearly the order does matter with a lock? If the "combination" to unlock something is 1-2-3. then why does order/position/type matter?ī.) If order does NOT matter with combinations. Order and Position DOES NOT matter.Ī.) If permutations are ALL ways of doing something. "Think of permutations as a list."Ĭombinations: Used for groups. Permutation: Every detail matters and ALL ways of doing something. Here are some of my understandings of each: There are basically infinite scenarios using these and every example problem/scenario I seem to convince myself it could be both! I see similar questions asked on here and obviously I did some research and read my book, but it seems like every explanation contradicts another in some way.
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