*Studying for a chapter examination is a personal process, one which nobody else can do for you. Simply take the time to review what you have done. *

**Here are the new terms in Chapter 12. **

Arrangement [12.1}

Binomial theorem [12.2}

Cards, deck of [12.2}

Combination [12.2}

Count-down property [12.1}

Distinguishable permutation [12.1}

Factorial [12.1}

Fundamental counting principle [12.1}

Instant Insanity [12.4}

Multiplication property of factorials [12.1}

Ordered pair [12.1}

Ordered triple [12.1}

Permutation [12.2}

Rubik’s cube [12.4}

Tree diagram [12.1}

*If you can describe the term, read on to the next one; if you cannot, then look it up in the text (the section number is shown in brackets).*

**IMPORTANT IDEAS **

*Can you explain each of these important ideas in your own words?*

Fundamental counting principle [12.1}

Multiplication property of factorials [12.1}

Formula for permutation [12.1}

Formula for distinguishable permutations [12.1}

Formula for combination [12.2}

Classify and identify counting techniques. [12.3}

Applications of counting (Rubik’s Cube and Instant Insanity) [12.4}

*Next, make sure you understand the types of problems in Chapter 12.*

**TYPES OF PROBLEMS**

Apply the fundamental counting principle. [12.1}

Simplify expressions involving factorials. [12.1}

Know the permutation formula. [12.1}

Evaluate permutations and distinguishable permutations. [12.1}

Know the combination formula. [12.2}

Evaluate combinations. [12.2}

Distinguish among a permutation, a combination, a distinguishable permutation, and the

fundamental counting principle. [12.3}

Answer applied counting questions. [12.1-12.3}

Use the notation involving Rubik’s cube [12.4}

Explain the Instant Insanity problem [12.4}

Once again, see if you can verbalize (to yourself) how to do each of the listed types of problems. Work all of **Chapter 12 Review Questions** (whether they are assigned or not).

Work through all of the problems before looking at the answers, and then correct each of the problems. The entire solution is shown in the answer section at the back of the text. If you worked the problem correctly, move on to the next problem, but if you did not work it correctly (or you did not know what to do), look back in the chapter to study the procedure, or ask your instructor. Finally, go back over the homework problems you have been assigned. If you worked a problem correctly, move on the next problem, but if you missed it on your homework, then you should look back in the text or talk to your

instructor about how to work the problem. If you follow these steps, you should be successful with your review of this chapter.

We give all of the answers to the Chapter Review questions

(not just the odd-numbered questions), so be sure to check your work with the

answers as you prepare for an examination.