Question 1189014: Find the number n of distinct permutations that can be formed from all the letters of each word:
a) THEM b) UNUSUAL c) SOCIOLOGICAL
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! a) THEM
Four unique letters ==> 4! = 4*3*2*1 = 24 unique arrangements
b) UNUSUAL
Seven letters where there are three U's, and four other letters. In this case we can compute as if all seven letters are unique AND THEN divide by the number of arrangements of the 3 U's that are indistinguishable:
7! / (3!) = 7*6*5*4*3*2*1 / (3*2*1) = 7*6*5*4 = 840
c) You should have enough to do this one.
Since there are multiple letters with more than one appearance, you will divide by the product of all those arrangements (for example, for the word REEPER, you would have 6! / (3!*2!) where the denominator comes from the 3 E's and 2 R's)
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