Question Video: Applications of the Counting Principle (Product Rule)

A construction company currently 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?

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Video Transcript

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.