SOLUTION: How many different 10-letter words (real or imaginary) can be formed from the letters in the word APPEARANCE?

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Question 607151: How many different 10-letter words (real or imaginary) can be formed from the letters in the word APPEARANCE?
Found 2 solutions by ewatrrr, MathLover1:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,Note correction

How many different 10-letter words (real or imaginary) can be formed from the

 letters in the word APPEARANCE?

APPEARANCE(10 Letter word)haveing highlight%283As%29,2Es,2Ps

 Ans: 10!/(3!2!2!) = 151,200

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

There are 10%21 unique arrangements of 10 different objects (the objects in this case are letters).
But since we have 3 A's, 2+P's and 2+E's, we must divide by the number of ways those can be rearranged creating indistinguishable combinations.
That is 3%21+%2A2%21%2A+2%21, meaning the answer is:
10%21+%2F+%283%21%2A+2%21%2A+2%21%29+=+3628800%2F24=151200