Answer:
Option D
Step-by-step explanation:
Given : Christina is randomly choosing 3 movies to take on vacation from 9 action movies, seven science fiction movies, and four comedies.
To find : Which statement is true?
Solution :
Total number of movies 9 + 7 + 4 = 20
The total number of combinations of choosing 3 movies from a pool of 20 is represented by ![^{20}C_3](https://tex.z-dn.net/?f=%5E%7B20%7DC_3)
Since there are 9 action movies in total and we're choosing 3, the number of combinations to do that is ![^{9}C_3](https://tex.z-dn.net/?f=%5E%7B9%7DC_3)
So the probability of choosing all action movies is the combinations of choosing all action movies divided by all the possible combinations of choosing any 3 movies from 20.
![=\frac{^{9}C_3}{^{20}C_3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5E%7B9%7DC_3%7D%7B%5E%7B20%7DC_3%7D)
Therefore, the probability of not choosing all action movies is
![=1-\frac{^{9}C_3}{^{20}C_3}](https://tex.z-dn.net/?f=%3D1-%5Cfrac%7B%5E%7B9%7DC_3%7D%7B%5E%7B20%7DC_3%7D)
Hence, Option D is correct.