Question

there are three highways from city a to city b, two highways from city b to city c, and two highways from city c to city d. how many different highway routes are there from city a to city d?

highway routes

Explanation:

Step1: Apply the multiplication principle

The multiplication principle states that if there are \(m_1\) ways to do the first task, \(m_2\) ways to do the second task, and \(m_3\) ways to do the third task, then the total number of ways to do all three tasks together is \(m_1\times m_2\times m_3\). Here, \(m_1 = 3\) (number of highways from \(A\) to \(B\)), \(m_2=2\) (number of highways from \(B\) to \(C\)), and \(m_3 = 2\) (number of highways from \(C\) to \(D\)).

Step2: Calculate the total number of routes

We calculate \(3\times2\times2\). First, \(3\times2=6\), then \(6\times 2 = 12\).

Answer:

\(12\)