4. Luis has 6 books: a novel, a biography, a dictionary, a self-help book, a statistics textbook and a comic book. a. In how many ways can all 6 books be ordered on a bookshelf? B. Luis' bookshelf has room for only 3 books. In how many ways can Luis choose and order 3 books, any order?c. Luis' bookshelf has room for only 3 books. In how many ways can Luis choose and order 3 books, in a specific order?

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.