There are 12 factorial or 479,001,600 permutations of the letters in the word SOCIOLOGICAL. However, since the letter O occurs three times, the letter I occurs twice, the letter L occurs twice, and the letter C occurs twice, you have to divide that by 8 (O), 2 (I), 2 (L), and 2 (C) giving you 7,484,400 distinctpermutations.
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64 different arrangements are possible.
There are 4 letters in IOWA, all non repeating. Arrangements are 4! or 24.
There are 6!/(3!*2!) = 60 arrangements.
There are 5!/2! = 60 arrangements.
5! 5 * 4 * 3 * 2 *1 = 120 arrangements you take the number of letters in the words and make it a factorial.