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cat
three
7 factorial
120?
There are 7 factorial, or 5,040 permutations of the letters of ALGEBRA. However, only 2,520 of them are distinguishable because of the duplicate A's.
The word mathematics has 11 letters; 2 are m, a, t. The number of distinguishable permutations is 11!/(2!2!2!) = 39916800/8 = 4989600.
None in either the Scrabble dictionary, or Webster's Second International dictionary. Both dictionaries contain over 250,000 words each.
That 'correct ordering' is usually called 'spelling'.
The correct ordering of the letters that make up a word is called the "spelling" of the word.
The solution is count the number of letters in the word and divide by the number of permutations of the repeated letters; 7!/3! = 840.
"spelling"
Take the total number of letters factorial, then divide by the multiple letters factorial (a and e). 7! / (2!*2!) or 1260.