How many ways are there to arrange the letters in STATISTICAL? My Work:
This is clearly a permutation so
I used $P(11; 2, 3, 2, 2, 1, 1) = 831600$ ways
Is my reasoning correct?
Well, STATISTICAL is a word of type 1232412456, i.e., $1^22^33^24^25^16^1$, and so the multinomial coefficient $$11\choose {2,3,2,2,1,1}$$ gives the result. Your reasoning is a bit short.
It is a permutation of multiset . There are three T's, two S's, two A's two I's,one C and one L.
$\dfrac{11!}{3!2!2!2!1!1!}$