Final answer:
Kelly can visit the 3 cities out of 4 in 24 different sequences, as calculated using the permutations formula 4! / (4 - 3)!, which equals 24.
Step-by-step explanation:
The question asks for the number of sequences of 3 cities that Kelly can visit from the top 4 biggest cities in Europe. Since the order in which Kelly visits the cities matters, this is a permutation problem. To calculate the number of sequences, you use the formula for permutations without repetition, which for selecting r items from a set of n items is given by n! / (n - r)!.
In this case, Kelly wants to visit 3 cities out of the 4 biggest ones, so n = 4 and r = 3. Therefore, the number of sequences of 3 cities she can visit is calculated as:
4! / (4 - 3)! = (4 × 3 × 2 × 1) / (1) = 24.
There are 24 different sequences possible for Kelly to visit any 3 of the 4 biggest cities in Europe on her spring break.