On the interne, you find an Latin quiz with 10 matching vocabulary questions. Your 3 year oid niece randomily matches the words with the definitions. What is the probability that she makes 100 on the quiz? Does the order matter? \( \square \) Thistira \( \square \) combination Will all of the words be matched? \( \square \) Yes : Can we use factorials? \( \square \) No How many different ways can the answe key be arranged? \( \square \) \( P( \) all correct \( )= \) \( \square \) (Enter your answer as a reduced fraction using / for the fraction bar)

To determine the probability that your 3-year-old niece randomly matches all the vocabulary words correctly, we can approach this problem logically! Given that there are 10 vocabulary words and their corresponding definitions, there is only one correct match among the possible combinations. In this case, the total number of ways to match these definitions with the vocabulary words is given by \(10!\) (10 factorial), which equals 3,628,800. Thus, the probability of getting all matches correct is: \[ P(\text{all correct}) = \frac{1}{10!} = \frac{1}{3,628,800} \] This fraction represents the chance of her matching all the words correctly because there is only 1 favorable outcome (all matches correct) out of 3,628,800 possible outcomes. In its simplest form, this is already quite reduced! So, to answer your question comprehensively: \[ P(\text{all correct}) = \frac{1}{3,628,800} \]