Final answer:
To determine the number of sets of four books that can be chosen from a set of 13 books, use the concept of combinations. The formula to calculate combinations is C(n, r) = n! / (r!(n-r)!), where n is the total number of objects and r is the number of objects to choose. In this case, C(13, 4) = 715.
Step-by-step explanation:
To determine how many sets of four books can be chosen from a set of 13 books, we can use the concept of combinations. The number of combinations of choosing r objects from a set of n objects is given by the formula: C(n, r) = n! / (r!(n-r)!). In this case, we want to choose 4 books from a set of 13 books, so the formula becomes C(13, 4) = 13! / (4!(13-4)!). Simplifying this expression gives us: C(13, 4) = 13! / (4!9!).
Now, we need to calculate the factorial of 13, 4, and 9. The factorial of a number is the product of all positive integers less than or equal to that number. We can use the formula: n! = n * (n-1) * (n-2) * ... * 3 * 2 * 1.
Therefore, C(13, 4) = 13 * 12 * 11 * 10 / (4 * 3 * 2 * 1 * 9 * 8 * 7 * 6 * 5) = 715. So, there are 715 sets of four books that can be chosen from a set of 13 books.