![]() ![]() Where m m m is the amount of possible outcomes of the first event, and n is the amount of possible outcomes of the second event. Possible outcome combination for events occurring = m × n \, m \ \times \ n m × n Equation 1: Fundamental counting principle In simple words, the fundamental counting principle says that: "If there are m possible ways for an event to occur, and n possible ways for another event to occur, then there are m × n m \times n m × n possible ways for both events to occur". This principle uses the multiplication of the possible outcomes of simultaneous combined events in order to produce the total amount of outcome combinations that can result from such events happening at the same time or needed for a certain process (you know, the events do not necessarily need to occur at exactly the same moment, but they need to occur for the particular desired process to yield a result). Thus, we define fundamental counting principle to solve for those processes! If you are eating only one, how many different desert options do you have to choose from? Let us make a tree diagram to find out:įigure 1: Tree diagram with the possible combinations to order a dessertįor this example we can clearly see that there are 6 different possibilities on the dessert you will end up enjoying, but imagine if there were many more options besides just cake and ice cream, and what if these other types of desserts had their own multiple options? We could still continue to count the different possible outcomes by drawing tree diagrams but these would get bigger and bigger, and even more difficult to manage. ![]() Types of dessert: cake and ice cream (2 types)įlavors of each dessert type: for cake = cheesecake, carrot cake, chocolate cake for ice cream = vanilla, strawberry, chocolate (3 flavors each). Let us look at a simple example of this: Imagine you go to a dessert bar and have a choice between eating cake or ice cream, besides that you know that the establishment offers 3 different kinds of each (cake and ice-cream), therefore you end up with the categories of: ![]() The basis of the counting principle can be easily explained with a tree diagram. In other words, if we have two or more different events (or categories) where each of them has a variety of possible outcomes occurring either at the same time, or in combination in order to produce a result, the fundamental counting principle provides a rapid manner of literally counting every single possible combination of outcomes from the combined events. The fundamental counting principle is a tool that helps us figure out the total possible outcomes of a combination of multiples events in a time-effective manner. What is the fundamental counting principle? Combinations and permutations are usually the main topics of study in this subject, but the basis for both starts with something denominated in the fundamental counting principle.Īnd so, in order to provide a deep introduction to combinatorics we start this chapter on our statistics course by studying what this fundamental principle is. Combinatorics is a branch of math that focuses on calculating total amounts of possible outcomes for a certain combination of events, or item categories which are finite and obey certain conditions.
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