Using the fundamental counting principle, determine the total number of outcomes of tossing three quarters and three pennies.
So here we have three quarters and three pennies. The fundamental counting principle reminds us that to find the total number of outcomes for a scenario, we multiply the total outcomes of each individual event together. That begs the question, how many individual events do we have in this scenario? You might think that there would be two individual events, the quarters and the pennies. But that is actually not the case. Each coin flip counts as its own individual event. So we have a total of six events in this problem. Each of the quarters and each of the pennies are a separate individual event.
Now that we know that we have six individual events, we can move on and we can figure out the outcome of each individual event, or the number of outcomes in each individual event. For my first quarter, what could the outcomes be? It could be heads or tails. Those are the two choices. The second quarter would also have two choices, heads or tails. That’s the same for the third quarter. The pennies also have two possible outcomes each. The pennies will land on heads or tails.
Now we can use our fundamental counting principle which tells us to multiply the total outcomes of each individual event. Here we multiply two times two times two times two times two times two. We could also write that as two to the sixth power. And two to the sixth power equals 64.
The total number of possible outcomes for tossing three quarters and three pennies is 64.