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