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Video: Applications of the Counting Principle (Product Rule)

Kathryn Kingham

Use the fundamental counting principle to determine the total number of outcomes of picking out an outfit from 4 shirts, 8 pairs of pants, and 2 jackets.

01:40

Video Transcript

Use the fundamental counting principle to determine the total number of outcomes of picking out an outfit from four shirts, eight pairs of pants, and two jackets.

Now we have to remember what the fundamental counting principle says. If event 𝑀 has π‘š possible outcomes and event 𝑁 has 𝑛 possible outcomes, then event 𝑀 followed by event 𝑁 has π‘š times 𝑛 possible outcomes.

In this problem, we have three separate events. First, you need to choose your shirt, then a pair of pants, and then your jacket. That means that we’ll need to multiply our choices for shirts, our choices for a pair of pants, and our jackets.

How many possible outcomes are there for the choice of what shirt to wear? Four, you have four shirts to choose from, so there are four possible outcomes.

The same goes for the pair of pants. How many possible outcomes? Eight, eight choices, eight possible outcomes. And finally our jacket choices, there are two.

Once we multiply all these things together, we’re left with 64. The total number of outcomes in picking four shirts, eight pair of pants, and two jackets is 64.