Question

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

Answer 1

do you mean permutations?

Answer 2

yes sorry

Answer 3

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

Answer 4

yes pretty much
you are trying to find all the different ways you can arrange the letters

Answer 5

ok I can do do it now that I understand it

Answer 6

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?

Answer 7

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?

Answer 8

it doesn't specify I would imagine it would have to include all 9 letters

Answer 9

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

Answer 10

ok thought so but wanted to make sure

Answer 11

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

Answer 12

You have 5 distinct objects with 9 places to put them. Interesting!!

Answer 13

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

Answer 14

To be honest, I really don't know how to solve it. I wish dumbcow would come back and enlighten us!

Answer 15

I believe that their is not 91 distinguishable arrangements. I am inclined to agree with the 45, but I am not positive ????

Answer 16

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

Answer 17

Gee who would of thunk it! lol, you don't have to list them I'll take your word for it.

Answer 18

Good grief I never would of thought of that lol!