1. Discrete Structures
Meeting 15
October 19, 2017

2. Question A More boxes (n) than things (k) Things are distinct
At most one thing per box
Count is (n choose k) times (k!)

3. Question B More boxes (n) than things (k) Things are the same
At most one thing per box
Count is (n choose k)

4. Question C (from the book)
Unlimited supply of things, each thing has one of k distinct labels.
n labeled boxes (the usual assumption)
Exactly one thing per box
Count is k times k times k … times k = kn
The Product Rule from Chapter 1

5. Question C (from class)
More things (k) than boxes (n)
Things are different
Exactly one thing per box
You overbought on Christmas presents
Count is (k choose n) times (n!)

6. Question D More things (k) than boxes (n) Things are the same
No restriction on the per box count
Becomes a stars and bars problem

7. Question E More things (k) than boxes (n) Things are different
For each of the boxes, j = 1,2, … n, the jth box gets kj things

8. Question F As many things (k) as boxes (n) Some things are the same
Each box gets exactly one thing
Count is k! with the repetitions removed
Anagrams of a word

9. Check Yourself, Pages
Answers are:

10. Overcounting with Adjustment
Deals with overlapping sets

11. Homework (1) For Tuesday (10/24): Sections 7.9 Problems:
These problems will be due on Thursday, 10/26
Each team is responsible for turning in a solution, written neatly, for each of its assigned four problems. See the Course Calendar for the assignment.
Each team is also responsible for solving the other 12 problems. The instructor is known to put homework problems on the Short Exams
Read Section 7.5, paying careful attention to the notation.
Be prepared to describe the template of each of the Try This! problems in Section That is, discover which of the questions A through F or PIE is the setting for the problem.

12. Homework (2) For Thursday (10/26): Read Sections 8.1 and 8.2
Do the Check Yourself on page 224