Mariah is randomly choosing three books to read from the following: 5 mysteries, 7 biographies, and 8 science fiction novels. Which of these statements are true? Check all that apply.

There are 20C3 possible ways to choose three books to read.
There are 5C3 possible ways to choose three mysteries to read.
There are 15C3 possible ways to choose three books that are not all mysteries.
The probability that Mariah will choose 3 mysteries can be expressed as 1/5C3
The probability that Mariah will not choose all mysteries can be expressed as 1 − 5C3/20C3

Question

chevy1234 chevy1234

09-06-2017
Mathematics

contestada

Mariah is randomly choosing three books to read from the following: 5 mysteries, 7 biographies, and 8 science fiction novels. Which of these statements are true? Check all that apply.

There are 20C3 possible ways to choose three books to read.
There are 5C3 possible ways to choose three mysteries to read.
There are 15C3 possible ways to choose three books that are not all mysteries.
The probability that Mariah will choose 3 mysteries can be expressed as 1/5C3
The probability that Mariah will not choose all mysteries can be expressed as 1 − 5C3/20C3

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joaobezerra joaobezerra · Answer 1 · 2021-08-20T00:32:18+02:00

Using the combinations formula and probability concepts, it is found that the correct options are:

There are 20C3 possible ways to choose three books to read.

There are 5C3 possible ways to choose three mysteries to read.

The probability that Mariah will not choose all mysteries can be expressed as 1 − 5C3/20C3

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Books are chosen without replacement, which means that the combinations formula is used to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]nCx = C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

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Sentence 1: There are 20C3 possible ways to choose three books to read.

3 books are chosen, from a set of 20. Thus, this sentence is correct.

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Sentence 2: There are 5C3 possible ways to choose three mysteries to read.

3 mysteries from a set of 5. Thus, this sentence is correct.

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Sentence 3: There are 15C3 possible ways to choose three books that are not all mysteries.

20 - 5 = 15 not mysteries, 3 chosen from this set. Thus, 15C3 possible ways to choose none mysteries. Since 1 or 2 mysteries are accepted, this sentence is wrong.

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Sentence 4: The probability that Mariah will choose 3 mysteries can be expressed as 1/5C3

Probability is number of desired outcomes divided by number of total outcomes.
5C3 ways to choose three mysteries.
20C3 total ways to choose.

Thus, the probability is: cand this sentence is wrong.

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Sentence 5: The probability that Mariah will not choose all mysteries can be expressed as 1 − 5C3/20C3

The probability of all mysteries is 5C3.
Thus, 1 - 5C3/20C3 probability of not all mysteries, and this sentence is correct.

A similar problem is given at https://brainly.com/question/4818951

ogmadlad ogmadlad · Answer 2 · 2021-09-17T14:11:06+02:00

ogmadlad ogmadlad

17-09-2021

Answer:

A B E

Step-by-step explanation:

A. There are 20C3 possible ways to choose three books to read.

B. There are 5C3 possible ways to choose three mysteries to read.

E. The probability that Mariah will not choose all mysteries can be expressed as 1 − 5C3/20C3

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