Question

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 StartFraction 1 Over 5 C 3 EndFraction.
The probability that Mariah will not choose all mysteries can be expressed as 1 − StartFraction 5 C 3 Over 20 C 3 EndFraction.

Answer 1

True:
- There are C(20,3) possible ways to choose three books (20 total books → C(20,3)=1140).
- There are C(5,3) ways to choose three mysteries (C(5,3)=10).
- The probability Mariah chooses 3 mysteries is C(5,3)/C(20,3)=10/1140=1/114, so the expression 1/(5C3) is incorrect.

False:
- There are C(15,3) ways to choose three books that are not all mysteries. (The correct count is C(20,3)−C(5,3)=1140−10=1130, not C(15,3)=455.)
- The probability she does not choose all mysteries is correctly 1 − C(5,3)/C(20,3), so that statement is true.