a Start by finding the number of routes from A to B, then the number of routes from B to C.
B
b Multiply the number of routes from A to C by the number of routes from C to D.
A
a 6 routes
B
b 12 routes
Practice makes perfect
a Consider the given diagram.
Using the Multiplication Counting Principle, we are asked to find the number of routes from A to C. This principle says that when having m ways of making a first selection and n ways to make a second selection, then there are m* n ways to make the two selections. With this in mind, let's first find the ways to go from A to B and then from B to C.
Note that there are 2 ways to go from A to B and 3 ways from B to C. Therefore, according to the Multiplication Counting Principle we have to multiply these values to get the number of routes from A to C.
2* 3=6 routes
b In this part we are asked to find the number of routes from A to D. Let's first find how many routes are from C to D.
The number of routes from C to D is 2. Additionally, we found that the number of routes from A to C is 6. Therefore, by using the Multiplication Counting Principle we can multiply these values to find the number of routes from A to D.
2*6=12 routes
