Illinois State University Mathematics Department

 MAT 409: Topics in Algebra and Combinatorics for K-8 Teachers

Twelve light bulbs
(4 identical red bulbs, 3 identical white bulbs, and 5 identical blue bulbs)
are to be installed in 18 sockets in a line,
resulting in 6 empty sockets.

How many arrangements are there for this install?

## Session 6: 20 February 2018

Basic Counting Strategies
Solving Equations Restricted to Non-Negative Integer Solutions (4.2)

Finding Fibonacci's Sequence Within Pascal's Triangle (4.1)

The Inclusion-Exclusion Principle (5.1)
Return Test #1 (Solutions)

Assignment #6

• Chapter 4 Section 1 (pp 105-116)
• Chapter 4 Section 2 (pp 116-128)
• Chapter 4 Learning From Others (pp 131-138)
• Chapter 5 Section 1 (pp 140-151)

Problems

• Chapter 3 Section 4 (pp 94-98): 14,20,27,39
• Chapter 4 (pp. 128-130): 1,4,5,8,9,14,21,25
• Chapter 4 Learning From Others (pp 131-138)

Early Send-Ins

• By 9:23 pm Sunday 2/25/18, email to me (day@ilstu.edu; write MAT 409 Assignment #6 as subject line) your responses to:
• Chapter 3.4: 14
• Chapter 4: 9,14,25
• Chapter 4 Learning From Others: (i) Read and respond to the prompt on the bottom of page 132 that refers to Solution 4; (ii) Read each prompt associated with Solutions 5, 6, and 7. Choose ONE of those prompts and respond, thereby analyzing ONE of the Solutions among Solutions 5, 6, and 7.

And Finally . . . Tentative Schedule for Remaining Tests (subject to change . . . )

• Test #2: Tuesday 3/20/18 (Session #10)
• Test #3: Tuesday 4/17/18 (Session #14)
• Semester Exam: Tuesday 5/8/18, 5:30 pm (as announced by ISU Registrar's Office)

Fundamental Components of a Problem-Solving Approach to Combinatorics Problems