Find the number of ways to form a two-digit number with no repeated digits, given four different digits to choose from.
To answer this question, we’re going to use something called the counting principle or the product rule for counting. This says that to find the total number of outcomes for two or more combined events, we multiply the number of outcomes for each event together. In this case, our events are the digits we choose for our two-digit number. That’s the first digit and the second digit. So, let’s consider the first set of outcomes, that is, the number of different ways we can choose the first digit.
We’re given four different digits, and so when we choose the first digit, we have four to choose from. But what about the second digit? Well, this is really important. We’re told that there are no repeated digits. We’ve already chosen one digit, so we can’t use that digit again. This means there are now three different numbers that we can choose from. So, there are four ways of choosing the first digit and three ways of choosing the second.
The product rule for counting says that to find the total number of outcomes, we multiply these values together. That’s four times three, which is equal to 12. And so, there are 12 different ways to form a two-digit number with no repeated digits, given four different digits to choose from.