Final answer:
The number of ways to arrange 15 books on a bedside table with the bible and a book of ghost stories at the ends is 2 multiplied by the factorial of 13, which equals 12,454,041,600 different arrangements.
Step-by-step explanation:
If we consider the issue of arranging 15 books on a bedside table where a bible and a book of ghost stories must go at the ends, we are dealing with a permutation problem. Since the two specified books must be at the ends, we do not consider their arrangement among themselves, which leaves us with 13 books to arrange freely.
The total number of arrangements for the 13 books that can freely be arranged is calculated by finding the factorial of 13, which is written as 13!. The formula for factorial is n! = n × (n-1) × (n-2) × ... × 3 × 2 × 1. Consequently, for 13 books, the calculation would be 13 × 12 × 11 × ... × 3 × 2 × 1.
However, since the bible and the book of ghost stories can each sit on either end, we have to account for two arrangements of these two books—either the bible at the beginning and the book of ghost stories at the end, or vice versa. Therefore, we multiply the number of arrangements for the 13 books by 2 to include the two possible arrangements of the two specified books at the ends.
Thus, the total number of ways the books can be arranged is 2 × 13!. This gives us 2 × 6,227,020,800, which equals 12,454,041,600 possible arrangements.