Final Answer:
The number of ways to arrange 4 different novels, 2 different mathematics books, and 1 biology book on a bookshelf, considering that the books can be arranged in any order, is given by the product of the factorial of the total number of books. Therefore, the answer is 7!, which equals 5040 ways.
Step-by-step explanation:
In combinatorics, the number of ways to arrange a set of distinct items is calculated using the factorial function. The factorial of a positive integer n, denoted as n!, is the product of all positive integers up to n. In this case, there are 7 books in total (4 novels, 2 mathematics books, and 1 biology book), so the number of ways to arrange them is 7!.
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040
This implies that there are 5040 different ways to arrange the books on the bookshelf. The multiplication comes from the fact that for each choice of book at a given position, there are progressively fewer choices for the remaining positions.
In conclusion, the total number of ways to arrange the 7 books is 5040, providing a comprehensive and accurate solution to the problem.