There are 4 customers who want to rent a car in San Francisco this evening. If there are only 3 cars still available, in how many different ways can the customers rent the cars?
Question
There are 4 customers who want to rent a car in San Francisco this evening. If there are only 3 cars still available, in how many different ways can the customers rent the cars?
Solution
To solve this problem, we can use the concept of permutations in combinatorics.
Step 1: Identify the number of items to choose from and the number to choose. Here, we have 4 customers and 3 cars.
Step 2: We are looking for the number of ways to assign 3 cars to 4 customers. This is a permutation problem because the order in which the cars are assigned matters.
Step 3: The formula for permutations is P(n, r) = n! / (n-r)!, where n is the number of items to choose from, r is the number to choose, and "!" denotes factorial.
Step 4: Substitute the given values into the formula. We get P(4, 3) = 4! / (4-3)! = 432*1 / 1 = 24.
So, there are 24 different ways the customers can rent the cars.
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