In the magical library of Hogwarts School of Witchcraft and Wizardry, there are three shelves dedicated to different genres of books: Potions, Charms, and Transfiguration. Each shelf is stacked with various books from famous authors in the wizarding world.
The Potions shelf contains 15 books written by the renowned potion master, Professor Phineas Crowley.
The Charms shelf has 12 books authored by the brilliant charm expert, Professor Felicity Flume.
The Transfiguration shelf showcases 18 books authored by the legendary transfiguration specialist, Professor Theodore Travers.
a) Hermione Granger wants to borrow one book from each shelf to study during her summer vacation. How many different ways can she choose one book from each genre?
b) Ron Weasley is only interested in borrowing books either from Professor Phineas Crowley or Professor Theodore Travers. In how many different ways can he choose two books for his summer reading?
c) Harry Potter is planning to borrow a maximum of three books from any of the shelves. How many different combinations of books can he select?
Note: Assume that the order of book selection matters, as each book has its unique content and insights to offer to the reader.
+42 We have to find
a) How many different ways she can choose one book from each genre.
b) How many different ways can he choose two books for his summer reading.
c) How many different combinations of books can he select.
a) Hermione Granger
Hermione wants to borrow one book from each shelf, so she has 15 choices for the Potions shelf, 12 choices for the Charms shelf, and 18 choices for the Transfiguration shelf. Since the order in which she chooses the books matters, we need to multiply these numbers to find the total number of ways she can choose one book from each shelf.
15 * 12 * 18 = 32,400
Therefore, Hermione can choose one book from each shelf in 32,400 different ways.
b) Ron Weasley
Ron only wants to borrow books from Professor Phineas Crowley or Professor Theodore Travers. This means he has 15 choices for the Potions shelf and 18 choices for the Transfiguration shelf. Since the order in which he chooses the books matters, we need to multiply these numbers to find the total number of ways he can choose two books.
15 * 18 = 270
Therefore, Ron can choose two books from either the Potions or Transfiguration shelves in 270 different ways.
c) Harry Potter
Harry is planning to borrow a maximum of three books from any of the shelves. This means he could borrow 0, 1, 2, or 3 books.
If Harry borrows 0 books, then there is only 1 way he can do this.
If Harry borrows 1 book, then he has 3 choices for which shelf to borrow the book from.
If Harry borrows 2 books, then he has 3 choices for which shelf to borrow the first book from, and then 2 choices for which shelf to borrow the second book from. This gives a total of 6 ways to borrow 2 books.
If Harry borrows 3 books, then he has 3 choices for which shelf to borrow the first book from, 2 choices for which shelf to borrow the second book from, and 1 choice for which shelf to borrow the third book from. This gives a total of 6 ways to borrow 3 books.
Therefore, Harry can borrow a maximum of 3 books in 1 + 3 + 6 = 10 different ways.
Therefore,
(a) Hermione Granger can choose one book from each shelf in 32,400 different ways.
(b) Ron Weasley can choose two books from either the Potions or Transfiguration shelves in 270 different ways.
(c) Harry Potter can borrow a maximum of 3 books in 10 different ways.
