Question

1. amusement park an amusement park has 12 major attractions: four roller coasters, two carousels, two drop towers, two gravity rides, and two dark rides. the park’s app will randomly select attractions for you to visit in order. what is the probability that the four roller coasters are the first four suggested attractions?

Explanation:

Step1: Probability of first roller coaster

There are 4 roller coasters out of 12 attractions. So the probability the first attraction is a roller coaster is $\frac{4}{12}$.

Step2: Probability of second roller coaster

After choosing one roller coaster, there are 3 left out of 11. So probability is $\frac{3}{11}$.

Step3: Probability of third roller coaster

Now 2 roller coasters left out of 10. Probability is $\frac{2}{10}$.

Step4: Probability of fourth roller coaster

1 roller coaster left out of 9. Probability is $\frac{1}{9}$.

Step5: Multiply the probabilities

To find the combined probability, multiply the probabilities from each step: $\frac{4}{12} \times \frac{3}{11} \times \frac{2}{10} \times \frac{1}{9}$.
Simplify the product: $\frac{4\times3\times2\times1}{12\times11\times10\times9} = \frac{24}{11880} = \frac{1}{495}$.

Answer:

$\frac{1}{495}$