How many disstinguishable perimeters can be formed from the letters in the word ARROGATOR?

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How many disstinguishable perimeters can be formed from the letters in the word ARROGATOR?

Mathematics
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do you mean permutations?
yes sorry
is it the same thing as seeing how many places you can move 12 people around?

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yes pretty much you are trying to find all the different ways you can arrange the letters
ok I can do do it now that I understand it
also what does it mean by distinguishable? Do I have to place them so everytime I come up wiht a different word not just letters?
depends on the problem are they looking for every possible word that can be formed or does each word have to include all 9 letters?
it doesn't specify I would imagine it would have to include all 9 letters
ok distinguishable means each word has to have a different combination of letters they dont have to be a real word First letter can be any one of the nine possible letters second letter can be any of the remaining 8 letters and so on
ok thought so but wanted to make sure
I would also think distinguishable means a perceived difference, note the double A, and O and the triple R. The fact that AARROGTOR and AARROGTOR has switched the A's it cannot be distinguishable, they appear the same, only I knew I used a different A lol
You have 5 distinct objects with 9 places to put them. Interesting!!
Radar so 5 *9? I thught it would be 9*9 because you have 9 letters and 9 places to put them all in a different order
To be honest, I really don't know how to solve it. I wish dumbcow would come back and enlighten us!
I believe that their is not 91 distinguishable arrangements. I am inclined to agree with the 45, but I am not positive ????
hmm yes radar you are correct, you could have 2 permutations that look the same i didn't account for that also the number of ways to arrange 9 objects is NOT 9*9 but 9! 9! is a factorial which means 9*8*7*6*5*4*3*2*1 this comes from there are 9 spaces to fill and there are 9 choices of letters for first space, after a letter is selected that leaves 8 letters to fill 2nd space, then 7 letters to fill 3rd space and so on... Now as we noted some of these arrangements really look the same as there are certain letters that are the same 3 R's 2 A's 2 O's to account for this we see how many ways we can arrange each of these letters for example for the A's A1A2 or A2A1 2*1 ways or 2! same for O's For the R's there are 3! ways to arrange them or 3*2*1 To discount these we divide answer = 9!/(3!*2!*2!) --> 9*8*7*6*5*4*3*2*1 / 3*2*1*2*1*2*1 do some cancelling -->9*8*7*6*5 = 15,120 distinguishable ways to arrange these letters
Gee who would of thunk it! lol, you don't have to list them I'll take your word for it.
Good grief I never would of thought of that lol!

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