In how many distinct ways can the letters of the word STATES be arranged?

1 Answer
MathFact-orials.blogspot.com
Jun 26, 2017

180

Explanation:

If we had 6 unique letters, such as STABLE, we'd be able to arrange the letters in #6! = 720# ways (we'd have 6 choices of what the first letter could be, 5 for the next letter, 4 for the next, etc... giving #6xx5xx4xx3xx2xx1 = 6!#

In our case, we have 2 sets of letters where there are more than 1 - we have two S's and two T's. And so we have to divide out the number of ways each of them can order #(S_1TATES_2# is the same as #(S_2TATES_1)# and so we'll have:

#(6!)/(2!2!)=(6xx5xx4xx3xx2!)/(2xx2!)=180#

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