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I need help on this question, it come sup often in one form or another in mathcounts, so I need to know how to solve it

There are 5 letters, 3 of each, take out 10. AAA, BBB, CCC, DDD, EEE. You do not replace letters after taking one out, and order does matter. How many ways to arrange the letters are there?

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You have a total of 15 letters in all.  It does not matter they are repeat letters.  Just treat them as 15 different items.

You want to create an arrangement that consists of 10 spaces.

Think of having a scrabble tile holder that can fit only a row of ten pieces.  You go to grab a piece from a pile that has 15 scrabble tiles.

Write out 10 dashes or placeholders on a piece of paper.

In the first position you can pick out any one of 15 pieces.
In the second position you can pick out any one of  the 14 pieces left
In the third position you can pick out any one of the 13 pieces left
and so on.

Mathematically it would be 15x14x13x12x11x.......whatever it comes out to for 10 decreasing numbers.  Multiply them all together.

Hope that helps.

I know permutations, but I don't know how to do this...

? This is permutations, though. Follow the instructions to pare down the variables, multiply, done. :)

Well, since there are three of each letter, do you divide by a certain number at the end?

Not unless I misunderstand the question. (Which is entirely possible.)