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Answer:
There are 24 different routes that can be taken if he needs to travel from La Union to Makati City.
Please see the attached file for the illustration of the tree diagram.
Step-by-step explanation:
This problem is an application of the Fundamental Principles of Counting which is part of the Statistics and Probability Curriculum. This is one of the basics of combinatorics. It is important that we know how to determine the total possible outcomes of a particular event since these are useful in making conclusions or generalizations as you study higher-level statistics.
The fundamental principle of counting defines as if an even has [tex]n[/tex] possible outcomes or ways and another event as [tex]m[/tex] possible outcomes or ways, then there [tex]n \times m[/tex] possible outcomes or ways if these two events happen together. So basically, the total possible outcomes or ways, considering all of the events, is just the product of the individual outcomes.
So if there are 4 routes from La Union to Quezon City and 6 routes from Quezon City to Makati City, then there are 24 different routes that can be taken if he needs to travel from La Union to Makati City.
This is simply multiplying 4 by 6, as a result, we have 24.
Please check the attachment for the tree diagram.
Looking at the tree diagram. The routes from La Union to Quezon City are in different colors, namely, red, green, violet, and yellow. Let's label the route from Quezon City to Makati City with numbers 1, 2, 3, 4, 5, 6.
Listing all the possible routes, we will have the following.
Red1, Red2, Red3, Red4, Red5, Red6
Green1, Green2, Green3, Green4, Green5, Green6
Violet1, Violet2, Violet3, Violet4, Violet5, Violet6
Yellow1, Yellow2, Yellow3, Yellow4, Yellow5, Yellow6
Thus, there are 24 possible routes that Aaron can take.
To learn more about the fundamental principle of counting, go to
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