Chapter 10 Counting Methods and Probability - 10.1 Apply the counting Principles and Permutations - Guided Practice for Example 6 - Page 686: 10

$50400$

CINCINNATI has $10$ characters, out of which $C$ is repeated twice, $I$ and $N$ are repeated $3$ times and $A$ and $T$ appear once. Thus using the formula for permutations with repetitions, the number of distinguishable permutations of the letters in the word is: $\frac{10!}{3!3!2!}=50400$