An English teacher needs to pick 10 books to put on her reading list for the next school year, and she needs to plan the order in which they should be read. She has narrowed down her choices to 5 novels, 5 plays, 4 poetry books, and 7 nonfiction books.
If she wants to include all 4 poetry books, how many different reading schedules are possible?
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To find the number of different reading schedules, we need to determine the ways in which the books can be ordered while ensuring that all 4 poetry books are included.
Since the teacher has already decided to include all 4 poetry books, we can consider them as a single unit. So, we have a total of 1 poetry unit, 5 novels, 5 plays, and 7 nonfiction books.
To determine the number of different reading schedules, we need to arrange these units in a specific order. The total number of books is 1 + 5 + 5 + 7 = 18.
To calculate the number of different schedules, we use permutations since the order matters. The formula for permutations is:
P(n, r) = n! / (n - r)!
Where n is the total number of items and r is the number of items we want to arrange.
In this case, we have 18 total books and we want to arrange all of them, so r = 18.
P(18, 18) = 18! / (18 - 18)! = 18! / 0! = 18!
Calculating 18! may be tedious, so it's more practical to use a calculator or computer program to get the value. In this case, 18! = 6,402,373,705,728,000.
Therefore, there are 6,402,373,705,728,000 different reading schedules possible for the English teacher's selections.