Video Transcript
How many three-digit numbers can be
formed by picking the units digit from the set containing the number eight, the tens
digit from the set containing the numbers eight, six, one, two, and the hundreds
digit from the set containing the numbers two, six, one?
We’re looking to create as many
three-digit numbers with this criteria as possible. What we’re not going to do is list
out all possible options because there might be quite a lot of them. Instead, we’re going to use 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 of each event together. In this case, each event is the
digit we end up picking, so the digits for the units column, the digits for the tens
column, and the digits for the hundreds column.
So let’s look at all our possible
options. We’ll begin with the hundreds
column. There are one, two, three numbers
in our set. And so there are three ways of
choosing the hundreds digit. Next, we’ll consider the tens
digit. There are one, two, three, four
numbers in this set. And so there are four ways of
choosing the tens digit. Finally, the units digit. Well, there’s only one number in
this set. So there’s only one way to choose
the unit digit.
The product rule says that to find
the total number of outcomes — in this case, the total number of three-digit numbers
— we multiply these values together. That’s three times four times one,
which is 12. And so we see that there are 12
different three-digit numbers that we can form by picking the units digit from the
set containing the number eight, the tens digit from the set containing the numbers
eight, six, one, two, and the hundreds digits from the set containing the numbers
two, six, and one.
