Chapter 10 Counting Methods and Probability - 10.2 Use Combinations and the Binomial Theorem - 10.2 Exercises - Quiz for Lessons 10.1-10.2 - Page 697: 6

$3780$

The word has $9$ characters, out of which $T$ appears once, $N,S$ appear twice and $E$ appears $4$ times. Thus using the formula for permutations with repetitions, the number of distinguishable permutations of the letters in the word is: $\frac{9!}{2!2!4!}=3780$