SOLUTION: List three permutations of the letters in the word STATISTICS, and how many different permutations of the letters in STATISTICS are there?

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Question 1155081: List three permutations of the letters in the word STATISTICS, and how many different permutations of the letters in STATISTICS are there?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
STATISTICS


ACIISSSTTT
TTTSSSIICA
ATCTITISSS

There are 10 letters, some distinguishable some indistinguishable.
There are 2 indistinguishable I's.
There are 3 indistinguishable S's.
There are 3 indistinguishable T's.

The formula for the number of distinguishable permutations is a fraction.

The numerator of the fraction is the factorial of the number of letters,
whether distinguishable or indistinguishable.

The denominator of the fraction is the product of the factorials of each
of the numbers of indistinguishable letters.

So the answer is this fraction 

10%21%2F%282%213%213%21%29

which we simplify:

3628800%2F%282%2A6%2A6%29=50400%29

Edwin