sum rule
The sum rule is a fundamental principle in mathematics that allows us to find the total number of outcomes when considering multiple independent events
The sum rule is a fundamental principle in mathematics that allows us to find the total number of outcomes when considering multiple independent events.
The sum rule states that if there are m ways of doing one thing and n ways of doing another thing, then there are m + n ways of doing either one of the two things.
To illustrate, let’s consider a simple example:
Suppose we have two different shirts, blue and red, and three different pants, black, grey, and khaki. We want to find out how many different outfits we can create by combining a shirt with a pair of pants.
To apply the sum rule, we count the number of choices for each item separately and then add them together.
Number of choices for shirts (m) = 2 (blue, red)
Number of choices for pants (n) = 3 (black, grey, khaki)
According to the sum rule, the total number of different outfits we can create is m + n = 2 + 3 = 5.
Therefore, we can create 5 different outfits by combining the two shirts and three pairs of pants available.
Note that the sum rule can be extended to more than two events. If we have additional items, like shoes and accessories, we can apply the sum rule successively to calculate the total number of possible combinations.
In summary, the sum rule is a fundamental principle in counting that allows us to find the total number of outcomes when considering multiple independent events by adding the number of choices for each event together.
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