1. Quiz 4 Counting: 4.3, 4.4, 4.5

2. Quiz4: May 5, 3.30-3.45 pm Your answers should be expressed in terms of factorials and/or powers. Imagine you want to buy books from a bookstore. The bookstore carries 20 titles, but it has 10 copies for each title. Your budget allows you to buy 9 books. a) How many combinations of books can you buy if the books with the same title are indistinguishable, but you are allowed to buy the same title more than once? b) How many combinations if all books are distinguishable and you can buy the same title more than once? c) How many combinations if you are not allowed to buy the same title twice and the books are still distinguishable. Next you decide to put your 9 distinguishable books into 3 distinguishable boxes, 3 books each. d) How many ways are there to do this? e) How many ways if the boxes are indistinguishable?

3. Quiz4: May 5, Answers Imagine you want to buy books from a bookstore. The bookstore carries 20 titles, but it has 10 copies for each title. Your budget allows you to buy 9 books. a) How many combinations of books can you buy if the books with the same title are indistinguishable, but you are allowed to buy the same title more than once? Combination with repetition: C(20+9-1,9). b) How many combinations if all books are distinguishable and you can buy the same title more than once? Combination without repetition: C(200,9). c) How many combinations if you are not allowed to buy the same title twice and the books are still distinguishable. First pick the title (combination without repetition): C(20,9). Next, pick the actual book, given the title: C(10,1). Total: C(20,9)x10. Next you decide to put your 9 distinguishable books into 3 distinguishable boxes, 3 books each. The order does not matter. d) How many ways are there to do this? 9!/(3!x3!x3!) e) How many ways if the boxes are indistinguishable? 9!/(3!x3!x3!x3!)