Fundamental principle of counting

Question

I have this question,

The number of different words that can be formed using all the letters of the word “MATHEMATICS” are?

I solved using the logic that if there are total 11 places so at all the 11 places all the 11 words can come, which gives me 11 to the power 11which is then divided by $2!*2!*2!$ due to the words M, T and A appearing 3 times.

But the actual solution is $11!/(2!*2!*2!)$, why did they consider “not repetition” ?

Answer 1

Your power means repetition. $11^{11}$ is the cardinal of a cartesian product $X\times\cdots\times X$ (11 times). of a set $X$ with 11 elements.