I'd like to point out that this is NOT homework. The question I'm asking is a question of my own creation based off of a question that I had in maths that I 'misunderstood' (read: overcomplicated) and spent ages being frustrated on only to realise that it was incredibly straight forward. However after creating this horrid question from hell I decided I wanted an answer to it anyway.
My question:
You have every letter in the alphabet from A-Z all in a line. You pick 5 random letters (let's just say A, B, C, D, and E to make it simple) and decide that these letters CAN NOT appear next to each other AT ALL. Any permutation of all 26 letters that has any of those 2 letters (A, B, C, D or E) next to each other does not count as a valid permutation. Any permutation that has 3 of those letters next to each other does not count, and so on and so forth. Permutations that have two of those letters next to each other, and another two (or three) of those letters next to each other somewhere else in the mixture are also not allowed. And, of course, having them ALL next to each other is not allowed.
How many permutations can be made?
So far I have:
[b]26!-((25!*(5!/3!))+(24!*(5!/2!))+(23!*(5!/1!))+(22!*(5!/0!)))[/b]
However that would only give me the answer when groups of 2, OR 3, OR 4, OR 5 aren't allowed. I've got to account for groups of 2 AND 3. I assume I should also be subtracting [b]'2!3!23!'[/b] (and I'd assume 2!2!24!, too) from [b]26![/b], however I'm not sure if that's correct (wouldn't '2!3!23!' also need to be multiplied by 5 (or 5!?) to account for the possible number of permutations of all the 5 letters?).
I know we have some mathematically inclined minds here, so any help would be appreciated as I'm really trying to understand this as best I can.
I understood at the start, permutations and such...then you lost me.
:( I hope JohnnyMo or aVoN or someone comes in here.
Come on, somebody must be able to help here.
What's a permutation? :downs:
If only I understood your question first.
Also am I the only one who read "premutation" as "premature ejaculation"?
[QUOTE=Hamushka11;17207344]Also am I the only one who read "premutation" as "premature ejaculation"?[/QUOTE]
yeah im pretty sure youre the only one
[QUOTE=Hamushka11;17207291]What's a permutation? :downs:[/QUOTE]
An arrangement of objects in which the order matters. So, for example, if you have three numbers, 1, 2 and 3, you have 6 permutations.
123
132
213
231
312
321
That's the maximum number of arrangements that you can have with 3 objects (which is noted as 3! (which means 3*2*1)). And, if you're wondering why it's 3*2*1 it's because, for your first choice you have 3 numbers to pick from. For your second choice you only have two numbers left to choose from, then, for the last choice you only have a single number left to pick from (so 3*2*1).
[QUOTE=RAWRrrr;17193056]I understood at the start, permutations and such...then you lost me.[/QUOTE]
This. I haven't needed to use a permutation/combination for anything since my final class of Algebra.
Did anyone else see "Math regarding premature ejaculations" ?
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