using the fundamental counting principle with three or more groups of items
There are three highways from city A to city B, two highways from city B to city C,and four highways from city c to city D. How many different highway routes are there from city A to city D?
To find the number of different highway routes from city A to city D, we can use the fundamental counting principle by multiplying the number of options for each group of items.
From city A to city B, there are three highway options.
From city B to city C, there are two highway options.
From city C to city D, there are four highway options.
To find the total number of different highway routes, we multiply the number of options for each group:
3 highways from A to B x 2 highways from B to C x 4 highways from C to D = 24 different highway routes from city A to city D.
Therefore, there are 24 different highway routes from city A to city D.
To find the total number of different highway routes from city A to city D using the fundamental counting principle with three groups of items, we multiply the number of choices for each group together.
In this scenario, we have three groups of highways:
Group 1: Highways from city A to city B (3 choices).
Group 2: Highways from city B to city C (2 choices).
Group 3: Highways from city C to city D (4 choices).
To find the total number of different highway routes, we multiply the choices for each group:
Total number of highway routes = Choices in Group 1 * Choices in Group 2 * Choices in Group 3
= 3 * 2 * 4
= 24
Therefore, there are 24 different highway routes from city A to city D.
Similar to the pizza topping problem:
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