Happy 2014!

Sit somewhere new to start the new year!

The plan for this semester…

Think, Pair, Share

A clothing store has a line of apparel where you can pair any of the pants with any of the shirts. How many outfits can you make if there are 4 pairs of pants and 6 shirts?

Think, Pair, Share

You are making sandwiches for your class picnic. You have 2 types of bread (white and wheat), 3 types of meat (ham, turkey, and chicken), and 2 types of cheese (provolone and cheddar). How many types of sandwich can you make if every sandwich includes both meat and cheese?

Fundamental Principle of Counting

Multiply the number of possibilities of the first choice by the number of possibilities of the next choice

Think back to clothing example and Sandwich example…

Some more examples…

If I draw 4 card from a deck of cards how many different combinations can I get?

A computer password must be 8 characters long. The first 4 characters must be letters and the last 4 numbers. How many possible passwords are there?

What if you can’t repeat?

Some more…

The standard configuration for a Texas license plate is 1 letter followed by 2 numbers followed by 3 letters.

How many different license plates are possible if letters and numbers can be repeated?

What if they cannot be repeated?

Arrangements of things

Ten teams are competing in the final round of the Olympic four-person bobsledding competition. In how many ways can the bobsledding teams finish the competition (assuming no ties)

How many ways could the gold, silver, and bronze go?

Factorial

6! means 6 factorial, which means

6 times 5 times 4 times 3 times 2 times 1

>On the calculator

>>>Think about both cases for the bobsledding problem

Permutations*For when order Matters!

The total number or ways of arranging n objects, taking r at a time is given by

!

( )!n

n r r

nP P

n r

Examples…

How many ways can 8 dogs be arranged in a row of 3?

How many ways can you arrange 4 letters from the alphabet?

You are burning a demo CD for your band. Your band has 12 songs, but you only want to include 4 on the demo. How many ways can you do that?

!

( )!n

n r r

nP P

n r

Permutations with RepetitionThe total number or ways of arranging n objects where one object is repeated s1 times, another is repeated s2 times, and so on, is:

Examples:

How many different arrangements of the letters of the word HIPPOPOTAMUS are there?

How many ways can you rearrange the letters of the word Mississippi?

Combinations

*Use when Order DOES NOT matterThe total number of ways of selecting n objects, taking r at a time (order does not matter)

!

( )! !n

n r r

nnC C

rn r r

Examples…

Example:

How many ways can I select 3 friends out of my 10 best friends to take to Cancun?

I am going on a trip and pack 4 pairs of shorts, 5 t-shirts and 2 pairs of sandals. Assuming everything goes together, how many different outfits could be made?

!

( )! !n

n r r

nnC C

rn r r

Assignment-

Write your own problem along the lines of these that relates to your life in some way on the front of a piece of paper. Write the answer and your reasoning on the back.