Video Transcript
How many different ways can we
pick a team of one man and one woman from a group of 23 men and 14 women?
This scenario effectively has
two events. Event one is choosing one man
from a total of 23, and event two is choosing one woman from a total of 14. And so, we’re going to need to
recall the fundamental counting principle. This says that if A and B are
two independent events such that A has 𝑚 outcomes and B has 𝑛 outcomes, there
are a total number of 𝑚 times 𝑛 outcomes of these two events together. And so, the total number of
ways that we can pick a team of one man and one woman must be 23 times 14. We can use any method we want
really to perform this calculation. Let’s use a column method.
Three times four is 12. So, we put a two in this column
and we carry the one. Then, two times four is eight
and we add the one to get nine. Next, we’re going to do three
times one. But since the one is in the
tens column, this is just like doing three times 10, and so we add a zero. Three times one is three and
two times one is two. We’re going to add these
values. Two add zero is two, nine add
three is 12, so we’re going to carry a one, and two add one is three. And so, we see that there are
322 ways to pick a team of one man and one woman from a group of 23 men and 14
women.
