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

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

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

Combinations formula:

is the number of different combinations of x objects from a set of n elements, given by the following formula.

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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

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

A similar problem is given at link

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126

required rate of return = 0.166 = 16.6%