Video Transcript
Using the fundamental counting principle, determine the total number of outcomes of rolling nine number cubes.
Let’s begin by recalling what the fundamental counting principle actually tells us. The fundamental counting principle, which is sometimes called the product rule for counting, tells us that the total number of outcomes for two or more events is found by multiplying the number of outcomes of each event together. So we need to ask ourselves, what are the events we’re considering here? Well, in fact, we’re rolling nine number cubes. A number cube, of course, will have six faces. And each face will have a different number on it. A dice is an example of this. This has six faces with the numbers one through six.
And so, if we think about cube number one, we know that there are six possible outcomes when we roll that cube. Then we roll the second number cube and there are still six possible outcomes, where, of course, the outcome is the number that that cube displays when it’s rolled. We then roll cube number three, that’s our third event, and there are still a possible six outcomes. We carry on going until we’ve rolled all nine number cubes, and we find that every number cube we roll has six possible outcomes.
The fundamental counting principle tells us that the total number of outcomes of rolling these nine number cubes is the product of each number of outcomes. So, that is six times six times six and so on. In other words, it’s six to the ninth power. Six to the ninth power is 10,077,696. And so the fundamental counting principle tells us that the total number of outcomes of rolling nine number cubes is 10,077,696.
