How many ways are there to arrange the letters in STATISTICAL

Question

My Work:

This is clearly a permutation so

I used $P(11; 2, 3, 2, 2, 1, 1) = 831600$ ways

Is my reasoning correct?

Answer 1

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.