Chapter 12.6, Problem 12PPE

a.

To determine

To calculate: The number of routes from A to C.

Answer to Problem 12PPE

The number of routes are 2.

Explanation of Solution

Given information:

  

Formula used:

When events are independent, the number of outcomes can be found out by Multiplication Counting Principle.

If there are m ways to make a first selection and n ways to make a second selection then there are $m\times n$ ways to make the two selections.

Calculation:

According to the question,

The number of states are 3. That is A, B, and C.

Now, there are 2 routes to reach C from A. They are :-

  $$

Hence, number of routes are 2.

b.

To determine

To calculate: The number of routes from A to D.

Answer to Problem 12PPE

There are 2 ways.

Explanation of Solution

Given information:

  

Formula used:

When events are independent, the number of outcomes can be found out by Multiplication Counting Principle.

If there are m ways to make a first selection and n ways to make a second selection then there are $m\times n$ ways to make the two selections.

Calculation:

According to the question,

The number of states are 4. That is A, B, C and D.

Now, there are 2 routes to reach D from A. They are :-

  $$

Hence, number of routes are 2.