1. Use Combinations and the Binomial Theorem
Lesson 10.2
Algebra II

2. Agenda Fake Quiz Homework Review
Continue discussion about combinations and binomial theorem.
Homework: #2-11 pg 694
Quiz on Friday lessons 10.1 – 10.2

3. Fake Quiz
You walk into your local ice cream parlor; there are 3 different types of cone and 25 flavors of ice-cream.
You have a coupon for a free single scoop of ice-cream either in a bowl or a cone. How many choices do you have?
Your uncle is with you and he wants a 3 scoop bowl where the flavors are all different. How many different choices does he have?
Your aunt orders a 4-mini scoop cone all flavors are different and, like Johanna the order of scoops is important. How many different cones does she have to choose from?

4. Use Combinations and the Binomial Theorem
Back to Pizza.. When we were looking at selecting 3 toppings out of 5 toppings for a pizza we found that we had 10 different choices.. 5×4×3 3×2×1 =10

5. Use Combinations and the Binomial Theorem
5×4×3 3×2×1 =10 This can also be written as: 5×4×3×2×1 3×2×1×2×1 =10 Or 5! 3!2! We say that this is 5 𝐶 3 pronounced 5 choose 3. EXAMPLE SLIDE

6. Use Combinations and the Binomial Theorem
Formally… Combinations of n objects taken r at a time The number of combinations of r objects taken from a group of n distinct objects is denoted by 𝑛 𝐶 𝑟 = 𝑛! 𝑟!(𝑛−𝑟)! DEFINITION SLIDE

7. Use Combinations and the Binomial Theorem
Let’s look at the problem b from the fake quiz… 3 scoops from 25 flavors in a bowl… 25∗24∗23 3∗2∗1 Written as a combination…. 25 𝐶 3 = 25! 3!(25−3)! =2300 EXAMPLE SLIDE

8. Use Combinations and the Binomial Theorem
Do problems 1 and 3 from Practice 10.2 B.