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Happy 2014!

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? .

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Happy 2014!

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  1. Happy 2014! • Sit somewhere new to start the new year! • The plan for this semester…

  2. 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?

  3. 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?

  4. 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…

  5. 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?

  6. 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?

  7. 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?

  8. 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

  9. Permutations*For when order Matters! • The total number or ways of arranging n objects, taking r at a time is given by

  10. 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?

  11. Permutations with Repetition The total number or ways of arranging n objectswhere 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?

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

  13. 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?

  14. 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.

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