Chapter 6 Section 7Combinations and Permutations

Algebra 2 Notes – February 10, 2009

Warm-Ups: Candy Hearts ActivityWORK WITH A PARTNER

Step 1: Dump out your Candy Hearts. Count how many total hearts you have.

Step 2: Count how many of each color you have.

Step 3: Find each probability P(Purple) P (Orange or Green) P(Not White) P(Yellow)

Step 4: Eat candy and ENJOY!!!

Factorials Factorials:

Examples:

By Definition:

Permutations Permutation: an arrangement of items

in a particular order.

nPr : n items taken r at a timen = total itemsr = number of arrangements

Example: There are 4 brand new 16 year-olds waiting to have their pictures taken for their driver’s license. How many different ways can all four people be lined up?

More Permutations Example: Seven golfers play in a

tournament in Hawaii. First, second, and third place awards will be given out at the end of the tournament. How many different ways can those awards be handed out?

n (total items) = ? r (number of arrangements) = ?

nPr =

Permutations Permutation Formula:

Example: Imagine you’re cleaning your room. You have 9 books needing to be put away. How many different ways can you arrange those 9 books if there is only room for 5 books on your bookshelf?

n = ? r = ?

Combinations Combination: A selection of items in which order

doesn’t matter

Examples??? Can you think of anything? You’re at Inta Juice and you decide to order a “Pickett

Yourself” smoothie. There are 6 different fruits to choose from but you can only put 3 into your drink. How many different combinations of fruit can go into your smoothie?

Identify n and r from the problem:n = number of items to choose fromr = number of items being chosen

Combinations Combination Formula:

Evaluate the following combinations: 12C3 10C5 8C2

Combinations or Permutations?? Decide whether each of the following

problems is a combination problem or a permutation problem. How do you know? A reading course in world literature has 20 books

on it. In how many ways can you choose four books to read?

How many different nine-player batting orders can be chosen from a baseball squad of 16?

You’re making a CD. You have chosen 10 of your favorite songs but only have room for 4 more songs on the CD. How many different ways can you chose those 4 songs?

Homework #21

Pg 348 #1, 2, 10, 11, 21, 22, 29-32, 40, 56