Video Transcript
Use the fundamental counting principle to find the total number of outcomes of rolling four number cubes and tossing two coins.
The fundamental counting principle is a method we can use to find the number of all possible outcomes in a sample space. It tells us that if we have two independent events 𝐴 and 𝐵 and the number of possible outcomes for event 𝐴 is 𝑥 while the number of possible outcomes for event 𝐵 is 𝑦, then the total number of distinct possible outcomes for these two events together is the product 𝑥 multiplied by 𝑦. This can be extended to any number of independent events. To find the total number of outcomes, we find the product of the number of outcomes for each individual event.
In this problem, we have four number cubes and we have two coins. A cube has six faces, so assuming that each face is different from the others, there will be six possible outcomes for each of the four number cubes. A coin, on the other hand, has two faces, so there will be two possible outcomes for each of the two coins. The fundamental counting principle tells us that the total number of outcomes for these six events together is the product of the number of individual outcomes. So we have six multiplied by six multiplied by six multiplied by six multiplied by two multiplied by two. That is six to the fourth power multiplied by two squared, which is 5,184. So, using the fundamental counting principle, we found that the total number of outcomes when we roll four number cubes and toss two coins is 5,184.
