At the local deli you can add two toppings to your sandwich. Draw a tree diagram to show how many ways you can select two different toppings for your sandwich if your choices are pickles, lettuce, and tomatoes. Draw a tree diagram

Combinations

Permutation- An arrangement in which order is important

Permutation Notation:nPr

n = total number of items r = number choosing

When lining 3 people up in line does the order matter?

How about just selecting 3 people, does order matter than?

When putting books on a shelf, does order matter?

When selecting three books to read, does order matter?

Consider these....

Review:

Combinations-An arrangement in which order does not matter. (AB and BA are the same combination because the letters are the same and the order does not matter)

Example : Selecting sandwich toppings

having lettuce and tomato on a sandwich is the same as having tomato and lettuce

Combination NotationnCr

n = total number of items r = number choosing

Formula:nCr =

1.) 9C5 2.) 10C3 

3.) From a group of 5 students, 3 students will be chosen for a school technology committee. How many different combinations are

possible?

4.) At the local pizza place, they have 9 different topping. You can order a pizza with 3 different toppings for $10. How many different types of pizza can be made?

5.) The DJ has 40 songs from the 80's. He needs to play exactly 5 songs at the dance. How many 5 song combination can he make if the order he plays the songs does not matter?

Demonstrate Understanding

1.) 2.) 7C3

3.) You have 5 choices of sandwiches fillings. How many different sandwiches could you make by choosing three of the five fillings?

4.) Mr. Cataldi selects a committee of 4 students from 25 students. How many different committees could he make?

5.) Class officers are president, vice-president, secretary and treasurer. From a class of 25 students, how many different groups of officers could students elect?

Solve each using the counting principle, permutations or combinations.

6.) How many different 6 digit zip codes are possible if no digit can repeat?

7.) There are 12 dogs in a Frisbee contest. How many ways can there be a winner and a runner-up?

8.) Ralph has a choice of 5 different ice cream flavors. He is going to select 3 flavors. How many ways can he select 3 flavors?