Use Combinations and the Binomial Theorem Lesson 10.2 Algebra II

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

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?

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

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

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

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

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