Question

The intercity transit system is given as following: There are 3 roads leading from York to Castle, 5 roads leading from Castle to Oakville, and 7 roads leading from Oakville to Sunfield. How many ways are there to get from York to Sunfield?​

Answer 1

Using the Fundamental Counting Theorem, it is found that there are 105 ways to get from York to Sunfield.

What is the Fundamental Counting Theorem?

• It is a theorem that states that if there are n things, each with $n_1, n_2, \cdots, n_n$ ways to be done, each thing independent of the other, the number of ways they can be done is:

$N = n_1 \times n_2 \times \cdots \times n_n$

In this problem:

• Each step is independent.

• 3 roads leading from York to Castle, hence $n_1 = 3$.

• 5 roads leading from Castle to Oakville, hence $n_2 = 5$.

• 7 roads leading from Oakville to Sunfield, hence $n_3 = 7$.

Then, in total:

$N = 3 \times 5 \times 7 = 105$

There are 105 ways to get from York to Sunfield.

To learn more about the Fundamental Counting Theorem, you can take a look at https://brainly.com/question/24314866