Here are some examples of how to use the fundamental principle of counting:
In a restaurant, there are 4 kinds of soup, 12 entrees, 6 desserts, and 3 drinks. How many different four-course meals can a patron choose? the four choices can be made in 4, 12, 6, and 3 ways, respectively. Hence, applying the fundamental principle of counting, there are possible meals.
In a state lottery, a contestant gets to pick a four-digit number that does not contain a zero followed by an uppercase or lowercase letter. How many such sequences of digits and a letter are there? Each of the four digits can be chosen in 9 ways (i.e., 1, 2,…, 9), and the letter can be chosen in 52 ways (i.e., A, B,…, Z plus a, b,…, z). Hence, there are possible patterns.
A corporation is creating a musical logo consisting of four different ordered notes from the scale C, D, E, F, G, A, and B. How many logos are there to choose from? the first note can be chosen in 7 ways, but because reuse is not allowed, the next note can be chosen in only 6 ways. the remaining two notes can be chosen in 5 and 4 ways, respectively. Using the fundamental principle of counting, musical logos are possible. if reuse of notes is allowed, logos are possible