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01 Jun 2022, 01:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
46% (01:48) correct
54%
(01:43)
wrong
based on 153
sessions
History
Date
Time
Result
Not Attempted Yet
A student must choose a program of four courses from a menu of courses consisting of English, Algebra, Geometry, History, Art, and Latin. This program must contain English and at least one mathematics course. In how many ways can this program be chosen?
(A) 6
(B) 8
(C) 9
(D) 12
(E) 16
Are You Up For the Challenge: 700 Level Questions
(A) 6
(B) 8
(C) 9
(D) 12
(E) 16
Are You Up For the Challenge: 700 Level Questions
The four-course program must contain English.
So the student should choose three from a menu of five courses: Algebra, Geometry, History, Art, and Latin.
C(5,3)=C(5,2)=10
This program must contain at least one mathematics course: either Algebra or Geometry.
We need to subtract ineligible choices from 10 options.
There is only one ineligible choice: History, Art, and Latin
So the answer is 10-1=9, which is answer choice (C).
So the student should choose three from a menu of five courses: Algebra, Geometry, History, Art, and Latin.
C(5,3)=C(5,2)=10
This program must contain at least one mathematics course: either Algebra or Geometry.
We need to subtract ineligible choices from 10 options.
There is only one ineligible choice: History, Art, and Latin
So the answer is 10-1=9, which is answer choice (C).
General Discussion
01 Jun 2022, 02:05
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As English is compulsory it is not needed for calculating the answer. So instead of having to choose 4 in total, we now have 3 - one of which must be a mathematics course.
There are 2 math choices and 3 'other' courses. The two possible cases here are: 2 math courses are selected and 1 'other' course, or 1 math course and 2 'other' courses.
2 math courses selected:
Number of ways of selecting 2 math courses from 2: \(1\)
Number of ways of selecting 1 'other' course: 3[/m]
Total ways of selecting 2 math courses and 1 'other' course: \(3*1=3\)
1 math course is selected:
Number of ways of selecting 1 math courses from 2: \(2\)
Number of ways of selecting 2 'other' courses: \(3\)
Total ways of selecting 1 math courses and 2 'other' course: \(3*2=6\)
Total of ways of choosing 1 math course or 2:
\(3+6=9\)
Answer C
There are 2 math choices and 3 'other' courses. The two possible cases here are: 2 math courses are selected and 1 'other' course, or 1 math course and 2 'other' courses.
2 math courses selected:
Number of ways of selecting 2 math courses from 2: \(1\)
Number of ways of selecting 1 'other' course: 3[/m]
Total ways of selecting 2 math courses and 1 'other' course: \(3*1=3\)
1 math course is selected:
Number of ways of selecting 1 math courses from 2: \(2\)
Number of ways of selecting 2 'other' courses: \(3\)
Total ways of selecting 1 math courses and 2 'other' course: \(3*2=6\)
Total of ways of choosing 1 math course or 2:
\(3+6=9\)
Answer C
