Chapter 8, Problem 81RE

a.

To determine

To find: The number of Possible schedules that the student can create from the offerings.

Answer to Problem 81RE

Total number of ways $=T=216$

Explanation of Solution

Given information:

Table that represents the available courses that the student can choose form the open sections.

There are four sections in course Math $100$ .

So, choosing a section in Math $100$ course is of $4$ ways.

There are Three sections in course Economics $110$

So, choosing a section in Economics $110$ course is of $3$ ways

There are Six sections in course English $105$

So, choosing a section in English $105$ course is of $6$ ways

There are Three sections in course Humanities $101$

So, choosing a section in Humanities $101$ course is of $3$ ways

Therefore,

Total number of ways $=T=4\times 3\times 6\times 3$

  $\Rightarrow$ Total number of ways $=T=216$ .

b.

To determine

To find: The number of Possible schedules that the student can create from the offerings.

Answer to Problem 81RE

Total number of ways $=T=108$

Explanation of Solution

Given information:

Table that represents the available courses that the student can choose form the open sections.

Two of the Math $100$ sections are closed.

There are four sections in course Math $100$ .

But out of them wo of the Math $100$ sections are closed.

So, there will be only two sections remaining in Math $100$ .

So, choosing a section in Math $100$ course is of $2$ ways.

There are Three sections in course Economics $110$

So, choosing a section in Economics $110$ course is of $3$ ways

There are Six sections in course English $105$

So, choosing a section in English $105$ course is of $6$ ways

There are Three sections in course Humanities $101$

So, choosing a section in Humanities $101$ course is of $3$ ways

Therefore,

Total number of ways $=T=2\times 3\times 6\times 3$

  $\Rightarrow$ Total number of ways $=T=108$ .

c.

To determine

To find: The number of Possible schedules that the student can create from the offerings.

Answer to Problem 81RE

Total number of ways $=T=36$

Explanation of Solution

Given information:

Table that represents the available courses that the student can choose form the open sections.

Two of the Math $100$ sections are closed.

Four of the English $105$ sections are closed.

There are four sections in course Math $100$ .

But out of them two of the Math $100$ sections are closed.

So, there will be only two sections remaining in Math $100$ .

So, choosing a section in Math $100$ course is of $2$ ways.

There are Three sections in course Economics $110$

So, choosing a section in Economics $110$ course is of $3$ ways

There are Six sections in course English $105$

But out of them four of the English $105$ sections are closed

So, there will be only two sections remaining in English $105$

So, choosing a section in English $105$ course is of $2$ ways

There are Three sections in course Humanities $101$

So, choosing a section in Humanities $101$ course is of $3$ ways

Therefore,

Total number of ways $=T=2\times 3\times 2\times 3$

  $\Rightarrow$ Total number of ways $=T=36$ .