Question Video: Finding How Many Numbers Can be Made from 4 Digits

How many three-different-digit numbers could be formed from the set of digits {1, 2, 4, 9}?

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Video Transcript

How many three-different-digit numbers could be formed from the set of digits containing the elements one, two, four, and nine?

Remember the fundamental counting principle, sometimes called the product rule for counting, says that if A is an event that has 𝑚 outcomes and B is an event that has 𝑛 outcomes, the total number of outcomes of A and B together is the product of these. It’s 𝑚 times 𝑛. Now, in fact, we have three possible events here. We have the event which is choosing the first digit, the second event is choosing the second digit, and the third event is choosing the third digit. But the counting principle still holds, so we need to find out the number of outcomes we have for choosing each digit and then multiply these together.

There are four possible digits we can choose from. Those are one, two, four, and nine. And so, it’s quite clear to us that there are four different ways of choosing the first digit. Now, we’re told that they are three-different-digit numbers. So, let’s think about how we choose the second digit. Let’s say, for instance, the first digit we chose was the number one. We can no longer use that. And so, there are three different digits to choose from. The number of ways then of choosing our second digit is three. Similarly, let’s move on to the third digit. We’ve now already chosen two numbers out of the set of four. And so, that means that there can only be two numbers left to choose from.

And so, there are four ways of choosing the first digit, three ways of choosing the second, and two ways of choosing the third. The product rule for counting or the counting principle tells us that we can find the total number of outcomes by multiplying these together. That’s four times three times two, which is equal to 24. There are 24 three-different-digit numbers that could be formed from the set of digits one, two, four, and nine.

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