A construction company has
three active sites. There are 20 different ways to
drive from site A to site B. There are 16 ways to drive from
site B to site C. In how many ways can we drive
from site A to site C visiting site B on the way?
Let’s imagine we have these
three construction sites. We’re told that there are 20
ways to get from site A to site B and then 16 ways to get from site B to site
C. We need to work out the total
number of ways that we can get from site A to site B and then to site C. And to do so, we’re therefore
going to recall something called the fundamental counting principle. This says that if A is an event
that has 𝑚 outcomes and B is another event that has 𝑛 outcomes, then the total
number of outcomes for A and B combined is 𝑚 times 𝑛.
Our first event is driving from
site A to site B. So, there’s 20 different ways
of doing this. There’s 20 outcomes. Then, our second event is
driving from site B to site C, and we know that there are 16 outcomes. And so, the total number of
ways that we can drive from site A to site B and then to site C is 20 times 16,
which is 320. There are 320 different ways of
doing that journey.