What is the product rule in counting used for?

What is the product rule in counting used for?

• A. To add the number of choices across stages.
• B. To divide the total by the number of stages.
• C. To multiply the number of choices in each stage to get the total.
• D. To subtract irrelevant options.

Answer: (C)

The product rule counts outcomes when a process has several independent steps. If the first step has options and the second step has options, the total number of distinct results is the product of those counts, and you keep multiplying as more steps are added. This works because for each choice in the first step, you can pair it with every choice in the second step, and with every choice in any subsequent step, forming all possible combined outcomes. For example, if you’re choosing an outfit with a certain number of shirt options and a certain number of pants options, the total outfits equal the shirt options times the pants options. Adding those counts together would not account for every possible combination, and dividing or subtracting would not describe forming complete sequences of choices. The product rule gives the exact total by multiplying the number of choices at each stage.

The product rule counts outcomes when a process has several independent steps. If the first step has options and the second step has options, the total number of distinct results is the product of those counts, and you keep multiplying as more steps are added. This works because for each choice in the first step, you can pair it with every choice in the second step, and with every choice in any subsequent step, forming all possible combined outcomes.

For example, if you’re choosing an outfit with a certain number of shirt options and a certain number of pants options, the total outfits equal the shirt options times the pants options. Adding those counts together would not account for every possible combination, and dividing or subtracting would not describe forming complete sequences of choices. The product rule gives the exact total by multiplying the number of choices at each stage.