A State University's Mathematics Department offers three courses: Calculu Linear Algebra, and Discrete Mathematics, and the chairperson is trying t decide how many sections of each to offer this semester. The department is allowed to offer 45 sections total, there are 5000 students who would like to take a course, and there are 60 teaching assistants to teach them. Sections of Calculus have 200 students each, sections of Discrete Mathematics have 100 students each, and sections of Linear Algebra have 50 students each. Calculus sections are taught by a team of 2 teaching assistants, while Discrete Mathematics and Linear Algebra need only 1 teaching assistant per section. How many sections of each course should the chair schedule in order to offer all the sections that they are allowed to, accommodate all of the students, and give one teaching assignment to each teaching assistant? The number of Calculus sections is [A]. The number of Linear Algebra sections is [B]. The number of Discrete Mathematics sections is [C].

A State University's Mathematics Department offers three courses: Calculu Linear Algebra, and Discrete Mathematics, and the chairperson is trying t decide how many sections of each to offer this semester. The department is allowed to offer 45 sections total, there are 5000 students who would like to take a course, and there are 60 teaching assistants to teach them. Sections of Calculus have 200 students each, sections of Discrete Mathematics have 100 students each, and sections of Linear Algebra have 50 students each. Calculus sections are taught by a team of 2 teaching assistants, while Discrete Mathematics and Linear Algebra need only 1 teaching assistant per section. How many sections of each course should the chair schedule in order to offer all the sections that they are allowed to, accommodate all of the students, and give one teaching assignment to each teaching assistant? The number of Calculus sections is [A]. The number of Linear Algebra sections is [B]. The number of Discrete Mathematics sections is [C].

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Description: A State University's Mathematics Department offers three courses: Calculus.Linear Algebra, and Discrete Mathematics, and the chairperson is trying todecide how many sections of each to offer this semester. The department isallowed to offer 45 sectio

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Publisher:Erwin Kreyszig

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Concept explainers

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.

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A State University's Mathematics Department offers three courses: Calculus.
Linear Algebra, and Discrete Mathematics, and the chairperson is trying to
decide how many sections of each to offer this semester. The department is
allowed to offer 45 sections total, there are 5000 students who would like to
take a course, and there are 60 teaching assistants to teach them. Sections
of Calculus have 200 students each, sections of Discrete Mathematics have
100 students each, and sections of Linear Algebra have 50 students each.
Calculus sections are taught by a team of 2 teaching assistants, while Discrete
Mathematics and Linear Algebra need only 1 teaching assistant per section.
How many sections of each course should the chair schedule in order to offer
all the sections that they are allowed to, accommodate all of the students,
and give one teaching assignment to each teaching assistant?
The number of Calculus sections is [A].
The number of Linear Algebra sections is [B].
The number of Discrete Mathematics sections is [C].

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