12.2 Combinations and the Binomial Theorem

1. 12.2 Combinations and the Binomial Theorem Objective: SWBAT use combinations to count the number of ways an event can happen, and use the binomial theorem to expand binomials.

2. Combinations • If you roll a 5 on one 6-sided die and a 3 on another, does the order matter? • No! The number of combinations of objects taken from a larger group can be represented by:

3. Playing Cards • What is the number of ways that you can be dealt 5 cards from 1 deck of 52? • 2,598,960 different 5-card combinations.

4. Pascal’s Triangle Notice any Patterns? 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1

5. Binomial Expansion • The binomial theorem plays a great role in theoretical probability. • can be expanded using Pascal’s Triangle

6. Expand • Use Pascal’s Triangle!

7. You try • Expand

8. Assignment • Read 12.1 • Pg. 712 #6-16e, 18-34e, 45, 78-88e