.
There are 10 symbols in the word "STATISTICS";
of them, "S" has multiplicity 3;
"T" has multiplicity 3;
"I" has multiplicity 2;
"A" and "C" have multiplicity 1.
The number of all permutations of 10 items is 10! = 10*9*8*7*6*5*4*3*2*1.
The number of all distinguishable arrangements of letters is 10! / (3! * 3! * 2! * 2!).
The factorials in the denominator serve to account for repeating letters.
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See the lesson
- Arranging elements of sets containing indistinguishable elements
in this site.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic "Combinatorics: Combinations and permutations".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.