SOLUTION: How many different arrangements of the letters in the word "INDIANA"?

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Question 612447: How many different arrangements of the letters in the word "INDIANA"?
Found 2 solutions by ewatrrr, Edwin McCravy:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi, 

How many different arrangements of the letters in the word Indiana?

7 lettered word, 2-a's ,2-i's, 2=n's 

 7!/(2!2!2!) = 630 different arrangements

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
INDIANA
If the I's, N's and A's were distinguishable, the answer would be 7!.
But the 7! would count the I's, N's, and A's each 2! times too many.
Therefore, the answer is 7%21%2F%282%212%212%21%29 = 5040%2F%282%2A2%2A2%29 = 5040%2F8 = 630

Edwin