SOLUTION: HOW MANY DIFFERENT 10-LETTER WORDS(REAL OR IMAGINARY) CAN BE FORMED FROM THE LETTERS IN THE WORD REPETITION

Question 1160524: HOW MANY DIFFERENT 10-LETTER WORDS(REAL OR IMAGINARY) CAN BE FORMED FROM THE LETTERS IN THE WORD REPETITION
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Don't use all CAPS.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

For the word "repetition", we have 10 letters. So there are
10! = 10*9*8*7*6*5*4*3*2*1 = 3,628,800
different ways to arrange them, but only if we can tell the two 'e's apart, and the same goes for the 'i's and the 't's as well.

Since we can't distinguish these letters, we have to divide by 2! = 2*1 = 2 for each repeated letter. This is to avoid double counting per either the 'e's, 'i's or 't's.

So we have (3,628,800)/(2!*2!*2!) = (3,628,800)/(2*2*2) = 453,600 permutations when we cannot distinguish between the repeated letters mentioned above.

Final Answer = 453,600

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