________________________________________________ www.jasonmyhre.weebly.com Reflection 9.1 Only two units left to go! Based on what you’ve learned about yourself (and me) this year, give (at least) three pieces of advice for next year’s Algebra 2 students. ________________________________________________ Tell me anything and everything that you know about probability!

Apply the counting principle and permutations (10.1) Unit 9: Probability Target 9.1, Day 1 Apply the counting principle and permutations (10.1)

You are ordering pizza for an end-of-the-year party You are ordering pizza for an end-of-the-year party. You have to decide between 3 different toppings: cheese, sausage, or pepperoni. You also have to choose between 4 sizes: small, medium, large, or extra large. How many different possibilities are there? One approach to solving this problem is to use a tree diagram.

You are trying to decide on a flower arrangement for a wedding You are trying to decide on a flower arrangement for a wedding. There are 13 types of flowers, 15 types of vases and 20 types of ribbons to choose from. How many possible arrangements are there?

A license plate contains 6 characters (3 letters and 3 digits). Find the number of possible license plates if... a) You are allowed to repeat characters. b) You are not allowed to repeat characters.

How many different arrangements of the letters “ABC” are possible How many different arrangements of the letters “ABC” are possible? List them. These arrangements are called ___________________. Notice that the _______ of the letters matters! (“ABC” is different than “CBA”) In order to evaluate a permutation, we will use a new operation called a ______________ (!).

Ten runners are competing in a race Ten runners are competing in a race. In how many ways can the runners finish? In how many ways can 3 runners finish in 1st, 2nd and 3rd place?

The number of permutations of n objects taken/chosen r at a time: Twenty different dogs are competing for Best in Show. In how many different ways can 1st, 2nd, 3rd and 4th place be awarded?

How many distinguishable permutations of the word “EYE” are there? How many distinguishable permutations of the phrase “BANANA RAMA” are there? s represents the number of times a letter repeats. If there are different letters repeating, use more s’s!

Warm Up 9.1, Day 2 You are trying to figure out what to wear for prom. If you have 5 pairs of shoes to pick from, 12 shirts (or dresses), and 10 pairs of pants (or purses), how many outfits are possible? How many seven digit phone numbers are possible if digits… a) Can be repeated? b) Cannot be repeated? *Note: the first digit CANNOT be a zero. Mr. Myhre is using the random name generator to pick 5 students from a class of 30. How many different ways can 5 students be picked to answer questions in order? (without repetition)

Unit 9: Probability Target 9.1, Day 2 Use combinations (10.2)

You have a coupon for 2 free toppings on a pizza You have a coupon for 2 free toppings on a pizza. If there are 15 toppings to choose from, how many combinations of 2 pizza toppings are possible? When the ______ does not matter, it is called a _______________.

Permutation or Combination?! It’s time to play… Permutation or Combination?! Picking lotto numbers. Picking teams for a bracket. Picking flights to visit cities. Picking salad ingredients. Selecting candidates for a position like president, VP, treasurer, etc. Selecting people for a committee.

In some elections, people vote for a president and a vice president from a pool of candidates, such that the highest vote getter is elected president, and the runner up is elected vice president. If there are 30 candidates total, in how many ways can these two positions be filled?

You plan you read 5 books this summer You plan you read 5 books this summer. You’ve received 15 different recommendations from friends and teachers. How many arrangements of 5 books are possible?

Sometimes it will be necessary to “combine” separate combinations (or permutations) in order to get an answer. Remember this rule of thumb: If you say “and,” _________. If you say “or,” _________. Student council has 6 seniors, 5 juniors, 4 sophomores and 3 freshmen. How many different committees of exactly 2 seniors and 2 juniors can be made? How many different committees of at most 4 students can be made?

You are dealt 5 cards from a standard deck of 52 cards You are dealt 5 cards from a standard deck of 52 cards. How many different 5 card hands are possible? How many 5 card hands are possible that have at least 3 face cards? How many 5 card hands contain 3 Jacks and 2 other cards that aren’t Jacks?

Warm Up 9.3, Day 3 Come up with a situation that would involve permutations and a situation that would involve combinations. Explain. How many 5 card hands are possible that have at most 2 spades? How many 5 card hands are possible that contain 3 spades and 2 clubs?

Use the binomial theorem (10.2) Unit 9: Probability Target 9.1, Day 3 Use the binomial theorem (10.2)

Expand. Any desire to expand (x + y) to the 4th power? Or 6th? Or 11th?! If only there was a faster way…

Blaise Pascal (1623-1662) Born in France Mathematician Physicist Philosopher Pascal’s Triangle Look back at the binomials we just expanded. Notice anything?

Expand using the Binomial Theorem and Pascal’s Triangle.

Find the 4th term in the expansion of