Question Video: Applications of the Counting Principle and Combinations Mathematics

How many different ways can we pick a team of one man and one woman from a group of 23 men and 14 women?

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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.

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