An English teacher gave her class a choice of 5 books to read. She then asked each student to select any 3 of the books and list them in the order he or she will read them. How many different lists are possible?
Question
An English teacher gave her class a choice of 5 books to read. She then asked each student to select any 3 of the books and list them in the order he or she will read them. How many different lists are possible?
Solution
This problem can be solved using the concept of permutations in combinatorics.
Step 1: Understand the problem The problem is asking for the number of ways to arrange 3 books out of 5 in a specific order.
Step 2: Identify the type of problem This is a permutation problem because the order in which the books are read matters.
Step 3: Apply the formula for permutations The formula for permutations is nPr = n! / (n - r)!, where n is the total number of options, r is the number of options chosen, and "!" denotes factorial, which is the product of all positive integers up to that number.
Step 4: Plug in the numbers In this case, n = 5 (the total number of books) and r = 3 (the number of books each student must choose). So the calculation would be 5P3 = 5! / (5 - 3)!
Step 5: Calculate the factorial 5! = 5 * 4 * 3 * 2 * 1 = 120 (5 - 3)! = 2! = 2 * 1 = 2
Step 6: Divide to find the answer 120 / 2 = 60
So, there are 60 different lists possible.
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