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Christina is randomly choosing 3 movies to take on vacation from 9 action movies, seven science fiction movies, and four comedies. Which statement is true?

A.) The probability that Christina will choose three comedies can be expressed as 1/4C3
B.) The probability that Christina will choose three action movies can be expressed as 20C3/9C3
C.) The probability that Christina will not choose all comedies can be expressed as 1 - 4C3/20C4
D.) The probability that Christina will not choose all action movies can be expressed as 1 - 9C3/20C3

A little clarification on how you got the answer is much appreciated as well!

Question

02-06-2017
Mathematics

contestada

Help ASAP! Nobody has the right answer to this!

Christina is randomly choosing 3 movies to take on vacation from 9 action movies, seven science fiction movies, and four comedies. Which statement is true?

A.) The probability that Christina will choose three comedies can be expressed as 1/4C3
B.) The probability that Christina will choose three action movies can be expressed as 20C3/9C3
C.) The probability that Christina will not choose all comedies can be expressed as 1 - 4C3/20C4
D.) The probability that Christina will not choose all action movies can be expressed as 1 - 9C3/20C3

A little clarification on how you got the answer is much appreciated as well!

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ratedloco ratedloco · Answer 1 · 2017-06-02T19:52:50+02:00

ratedloco ratedloco

02-06-2017

Best answer to this would be the probability that Christina will choose three action movies can be expressed as 20C3/9C3 .

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tardymanchester tardymanchester · Answer 2 · 2019-03-11T06:33:51+01:00

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 [tex]^{20}C_3[/tex]

Since there are 9 action movies in total and we're choosing 3, the number of combinations to do that is [tex]^{9}C_3[/tex]

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.

[tex]=\frac{^{9}C_3}{^{20}C_3}[/tex]

Therefore, the probability of not choosing all action movies is

[tex]=1-\frac{^{9}C_3}{^{20}C_3}[/tex]

Hence, Option D is correct.