Christina is randomly choosing three movies to take on vacation from nine action movies, seven science fiction movies, and four comedies. which statement is true?

the probability that christina will choose three comedies can be expressed as .1/ 4^c3
the probability that christina will choose three action movies can be expressed as .20^c3/ 9^c3
the probability that christina will not choose all comedies can be expressed as 1 − 4^c3/ 20^c4.
the probability that christina will not choose all action movies can be expressed as 1 − 9^c3/20^c3

"The probability that Christina will not choose all action movies can be expressed as 1 − 9^C3/20^C3"

Step-by-step explanation:

The combination of choosing r things for m total things is given as mCr

In total, there are 9 + 7 + 4 = 20 movies

So choosing 3 movies from action movies will be 9C3

And choosing 3 movies from total number of movies is 20C3

Thus, probability of choosing action movies is:

Also, we know probability of something NOT happening is

1 - probability of that thing happening

Hence, probability that Christina WILL NOT CHOOSE all action movies is:

Correct answer choice is last option.

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