Answer:
To solve this problem, we need to find the number of ways to arrange the books on the bookshelf. This involves calculating the permutations of the books.
Part A: Arranging All 6 Books
The number of ways to arrange all 6 books is given by the formula:
$ \text{Number of permutations} = \frac{\text{Number of items}}{\text{Number of items}} = 6 $
Part B: Choosing and Ordering 3 Books
To choose and order 3 books, we need to select 3 books from the 6 available and arrange them in a specific order. This involves calculating the combinations of the books.
$ \text{Number of combinations} = \frac{\text{Number of items}}{\text{Number of items}} = \frac{6}{3} = 20 $
Part C: Choosing and Ordering 3 Books
To choose and order 3 books, we need to select 3 books from the 6 available and arrange them in a specific order. This involves calculating the combinations of the books.
$ \text{Number of combinations} = \frac{\text{Number of items}}{\text{Number of items}} = \frac{6}{3} = 20 $
Conclusion
The number of ways to arrange all 6 books is 720. The number of ways to choose and order 3 books is 20.
