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Fundamental Counting Principle Problem 

Vera Brito Delgado 

St. Thomas University 

Applied Statistics. STA 2023 AP1 

Dr. Freddy Suarez 




Fundamental Counting Principle Problem 


   The fundamental counting principle (FCP) is a mathematical formula frequently used to evaluate the total number of alternative arrangements of a set of objects. These calculations can only solve several probability problems (Yale National Initiative, n.d.). According to the Fundamental Counting Principle, if one event or decision has x possible outcomes or choices and another event has y possible outcomes or options, then the total number of distinct combinations of results between the two is equal to x*y (Nagwa, 2023).  

   For instance, five patients are in critical condition and need ICU care. However, the hospital can only admit three to the ICU at any time due to resource limitations. Using the Fundamental Counting Principle, I will find how many distinct ways the hospital can allocate the five patients among the three admissions allowed.   

   The number of options that are accessible for each phase in the process of allocating patients to the ICU must be determined to solve this problem by utilizing the Fundamental Counting Principle. There are five possible ways to choose a patient for the first admission. Four choices are available for the second admission because a patient has already taken the first admission. There are three options for the third admission since already two patients have been assigned to the first and second admission. Moreover, the total number of possible ways to allocate three admissions among five patients is 5*4*3=60. Furthermore, in this case, using the fundamental counting principle, the hospital can allocate the three admissions to the five patients in sixty different ways. As a result, these calculations can assist the hospital, healthcare professional, or nurse prioritize patient care needs depending on the severity and optimizing resource use. 



Mastin, L. (2020). Fundamental counting principle- Explanation and Examples. Story of mathematics. Retrieved https://www.storyofmathematics.com/fundamental-counting-principle 

Yale National Initiative. (n.d.). 18.04.09: Enumerating daily life with counting principles, permutations, and combinations. https://teachers.yale.edu/curriculum/viewer/initiative_18.04.09_u 

Statistics: Fundamental counting principle

Glenda Garrido Blanco 

St. Thomas University

STA-2023-AP1-Applied Statistics

Dr. Freddy Suarez

March 29, 2023


Fundamental counting principle

Suppose for a moment that you are responsible for choosing the various seating configurations for a restaurant that

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