Fundamental counting principle example12/9/2023 different ways respectively, the number of ways that all events can occur is equal to Using the above problem, we can generalize and write a formula related to counting as follows: It is clear from the tree diagram above that the total number N of choices may be calculated as follows: Let n3 be the number of choices of the mathematics course, here n3 = 2. Let n2 be the number of choices of the science course, here n2 = 2. Let n1 be the number of choices of the physics course, here n1 = 3. The total number of choices may be calculated as follows: The different ways in which the 3 courses may be selected are: Then the second column shows the 2 possible choices of the science course and the last column shows the 2 possible choices for the mathematics course. The first column on the left shows the 3 possible choices of the physics course: P1, P2 or P3. Let us use a tree diagram that shows all possible choices. In how many ways can this student select the 3 courses he has to take? He may choose one of 3 physics courses (P1, P2, P3), one of 2 science courses (S1, S2) and one of 2 mathematics courses (M1, M2). Let us start by introducing the counting principle using an example.Ī student has to take one course of physics, one of science and one of mathematics. Counting Problems With Solutions Counting Problems With SolutionsĬounting problems are presented along with their detailed solutions and detailed explanations.
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