The Five Counting Rules Every Student Should Know

In this story, we will go over 5 useful counting rules that will make your life very easy. As long as you understand which rule to use under which circumstance, this is a very straightforward topic. Now, let's dive straight into the 5 rules one by one!

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Rule 1

Example: If you roll a fair die 3 times, then there will be:

• A dice roll consists of 6 different mutually exclusive and collectively exhaustive outcomes (1, 2, 3, 4, 5 and 6), so k=6.

• n=3 because the dice were rolled 3 times.

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Rule 2

Example: There are 4 parks, 3 restaurants and 6 movie choices. In total, there would be

• You simply multiply the possible choices for each trial.

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Rule 3 (factorial)

Example: If you have 5 books, then you have:

• This should be a review of high school or even middle school math for some of you.

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Rule 4 (permutation)

You may also recall this rule as a permutation from secondary school.

Example: You have five books, and you are selecting three to put on the bookshelf. You would have:

Take note that the order of selection does matter in permutation!

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Rule 5 (combination)

You may recall this rule as a combination from secondary school.

Example: You have five books, and you are selecting three to read. The order in which you read does not matter. You would have:

Take note that the order of selection does not matter in combination!

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Conclusion

Simple, short and easy! These five counting rules will become useful from time to time. They will help you easily calculate seemingly difficult probability questions. In our next story, we will move on to a new topic and discuss the different types of distribution.