1. Warm Up: 2/21/2012 Use completing the square

3. Fundamental Counting Principles  If one selection can be made in m ways, and for each of these a second selection can be made in n ways, then the number of ways the two selections can be made is  If the possibilities being counted can be grouped into mutually exclusive cases, then the total number of possibilities is the sum of the number of possibilities in each case

4. EXAMPLE #1 Step 1: How many choices for model Step 2: How many choices for color Step 3: Multiply the number of choices A local moped dealer sells 6 different models of mopeds. Each model is available in 3 colors. How many combinations of model and color are there?

5. Example #2 How many odd 2-digit whole numbers less than 70 are there? Step1: how many choices for the tens’ digit Step 2: how many choices for the units’ digit Step 3: multiply the number of choices

6. Example #3 Step 1: How many choices for blouses Step 2: How many choices for scarves Step 3: Multiply the number of choices Elena can wear one of 2 blouses and one of 5 scarves. How many blouse-scarf combinations are available to her?

7. Example #4 How many positive integers less than 100 can be written using the digits 6, 7, 8, and 9? Step 1: number of outcomes for the 1 digit integers Step 2: number of outcomes for the 2 digit integers Step 3: Add the outcomes

8. Example #5 Step 1: Number of outcomes for 1- letter case Step 2: Number of outcomes for 2- letter case Step 3: Number of outcomes for 3- letter case Step 4: Add the outcomes How many license plates of 3 symbols (letters and digits) can be made using at least one letter in each?

9. Example #6 How many positive odd integers less than 10,000 can be written using the digits 3, 4, 6, 8, and 0 Step 1: How many 1 digit numbers Step 2: How many 2- digit numbers Step 3: How many 3- digit numbers Step 4: How many 4- digit numbers