Disclaimer: The number of cities in Asia will be 8 and not 888.
Elyse can choose from 960 different combinations of cities.
What are permutations and combinations?
The different ways in which objects from a set can be picked, often without replacement, to produce subsets are known as permutations and combinations. When the order of selection is a factor, this selection of subsets is termed a permutation; when order is not a factor, it is called a combination.
How do we solve the given question?
We are given 4 continents, with a number of cities to choose from for Elyse to visit.
The table is like this:
Continent Number of cities
Europe 10
Asia 8
Africa 4
Australia 3
We use permutations and combinations to find the number of combinations Elyse will have to choose from.
We can say that for every 10 cities in Europe, she can choose any of the 8 cities in Asia. Similarly, for every 8 cities in Asia, she can choose any of the 4 cities in Africa. And similar is the case for Africa and Australia.
∴ Elyse can choose from a combination of 10*8*4*3 cities,
or, Elyse can choose from a combination of 960 cities.
Learn more about permutations and combinations at
https://brainly.com/question/4658834
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