1. Sports Camp Morning Camp AerobicsRunningYogaSwimmingWeights Afternoon Camp HikingTennisVolleyballSoftball List all the possible choices available on your paper

2. Terminology of Counting 1) Tree Diagram 2) Outcome – number of ways it can occur. Each individual mix is an outcome. 3) Event – situation requiring choices (morning events, afternoon events) 4) Independent event – an event that does not affect or involve another event. Does not affect the outcome of a different event.

3. How many events? Outcomes? Diagram it 1. Flip a coin, then roll a number cube? Show all outcomes. 2. Choose from 5 movies, then from 3 restaurants? Show all outcomes. 3. Choose from 3 new vehicles and colors white, black or blue. Show all outcomes. 4. Roll a number cube, then pick a card from a deck of cards?

4. How many outcomes? Events? 1. Roll a number cube 4 times. How many possible? 2. License plates – 4 letters and 3 numbers. How many possible (can repeat #s and letters)? 3. Social security number – 9 digits, all repeatable. How many possible? 4. Social security number – 1 st and last digits must be 1 or 0. Other 7 may be anything. How many possible?

5. Counting Principle If one event occurs ‘m’ ways and second event occurs ‘n’ ways, then the 2 events occur n * m ways Provided the events are independent of each other.

6. Permutations

7. How many outcomes? 1) 18 bands compete to win 1 st, 2 nd, 3 rd, and 4 th place. How many outcomes possible? 2) President, vice-president, treasurer chosen from a class of 520. How many outcomes possible? On these questions, does order matter?

8. Permutations Arrangement of a group of objects in a particular order. (order matters!) 20 choose 3: means 20 * 19 * 18 means 20 * 19 * 18 Also written as 20 P 3 which means 20! 20!(20-3)!