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: 4

$120$

The word has $5$ characters, out of which $I,D,A,H,O$ appear once; thus using the formula for permutations with repetitions, the number of distinguishable permutations of the letters in the word is: $\frac{5!}{1!}=120$