mariah is randomly choosing three books to read from the following: 5 mysteries, 7 biographies, and 8…

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 $_{20}c_{3}$ possible ways to choose three books to read. there are $_{5}c_{3}$ possible ways to choose three mysteries to read. there are $_{15}c_{3}$ possible ways to choose three books that are not all mysteries. the probability that mariah will choose 3 mysteries can be expressed as $\frac{1}{_{5}c_{3}}$. the probability that mariah will not choose all mysteries can be expressed as $1 - \frac{_{5}c_{3}}{_{20}c_{3}}$.

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 $_{20}c_{3}$ possible ways to choose three books to read. there are $_{5}c_{3}$ possible ways to choose three mysteries to read. there are $_{15}c_{3}$ possible ways to choose three books that are not all mysteries. the probability that mariah will choose 3 mysteries can be expressed as $\frac{1}{_{5}c_{3}}$. the probability that mariah will not choose all mysteries can be expressed as $1 - \frac{_{5}c_{3}}{_{20}c_{3}}$.

Answer

Explanation:

Step1: Calculate total number of books

There are (5 + 7+8=20) books. The number of ways to choose 3 books out of 20 is given by the combination formula ({n}C{r}=\frac{n!}{r!(n - r)!}), so there are ({20}C{3}) ways to choose 3 books.

Step2: Calculate ways to choose 3 mysteries

There are 5 mysteries. The number of ways to choose 3 mysteries out of 5 is ({5}C{3}).

Step3: Calculate ways to choose non - all - mysteries

The number of ways to choose 3 books that are not all mysteries is the total number of ways to choose 3 books minus the number of ways to choose 3 mysteries. The total number of ways to choose 3 books is ({20}C{3}) and the number of ways to choose 3 mysteries is ({5}C{3}), not ({15}C{3}).

Step4: Calculate probability of choosing 3 mysteries

The probability of choosing 3 mysteries is (\frac{{5}C{3}}{{20}C{3}}), not (\frac{1}{{5}C{3}}).

Step5: Calculate probability of not choosing all mysteries

The probability of choosing all mysteries is (\frac{{5}C{3}}{{20}C{3}}), so the probability of not choosing all mysteries is (1-\frac{{5}C{3}}{{20}C{3}}).

Answer:

There are ({20}C{3}) possible ways to choose three books to read. - True There are ({5}C{3}) possible ways to choose three mysteries to read. - True There are ({15}C{3}) possible ways to choose three books that are not all mysteries. - False The probability that Mariah will choose 3 mysteries can be expressed as (\frac{1}{{5}C{3}}). - False The probability that Mariah will not choose all mysteries can be expressed as (1 - \frac{{5}C{3}}{{20}C{3}}). - True

So the correct statements are:

  • There are ({20}C{3}) possible ways to choose three books to read.
  • There are ({5}C{3}) possible ways to choose three mysteries to read.
  • The probability that Mariah will not choose all mysteries can be expressed as (1 - \frac{{5}C{3}}{{20}C{3}}).