Slimp's Bookstore receives a box of books from each of five paperback publishers. Each box contains 24 different titles. The store manager decides there is room to display 4 books from each of 3 of the publishers. How many ways can the display be chosen?
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First he chooses the publishers in one of 5c3 = 10 ways.
For each of the 3, he can choose 4 books from 24 in one of 24c3 = 2024 ways.
So he can choose 12 books in one of
10 * 2024^3 ways = about 83 billion.
That would answer the simplest interpretation of the problem -
just how many ways books can chosen.
If the chosen books are then put on display in some specific order,
we multiply that by
(3 * 4) ! = 12! = 479,001,600 or close to 500 million.
Then multiplying everything together you get 3.97162731 × 10^19
Let's hope he decides before pondering each one.
For each of the 3, he can choose 4 books from 24 in one of 24c3 = 2024 ways.
So he can choose 12 books in one of
10 * 2024^3 ways = about 83 billion.
That would answer the simplest interpretation of the problem -
just how many ways books can chosen.
If the chosen books are then put on display in some specific order,
we multiply that by
(3 * 4) ! = 12! = 479,001,600 or close to 500 million.
Then multiplying everything together you get 3.97162731 × 10^19
Let's hope he decides before pondering each one.