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					                 Lunch Specials

“Choose 1 Entrée, 2 Side Dishes and a Drink”
       Entrée                              Side Dish
 •   Pizza                         •       Salad
 • Ravioli                         • Pasta Salad
 • Spaghetti                       • Potato Salad
 • Lasagna                         • Chips


                          Drink
 •   Coke        •   Sprite            •   Iced Tea
 •   Root Beer   •   Fruit Punch
     Fundamental Counting Principle



      4 •     4       • 3 •        5
    Entree   Side 1   Side 2   Drink
                                        = 240 different choices


•   Pizza              •   Salad             •   Coke
• Ravioli              • Pasta Salad         • Root Beer
• Spaghetti            • Potato Salad        • Sprite
• Lasagna              • Chips               • Fruit Punch
                                             • Iced Tea
CA STANDARDS:
18.0 Students use fundamental counting principles to compute combinations
and permutations

 Learning Objectives: Students use (1) factorials and (2) permutations.


                     Agenda: 03/21/13
  1.) Warm-up
  2.) Questions:
        WS Prob. I-1
        WS Prob. I-2
        WS Prob. I-3
  3.) Lesson Factorial (ppt.)
  4.) Class/Homework:

  5.) Work With Your Neighbor
       STAY ON TASK!!!
  Factorials        - Is the product of all the integers between
                       1 and n.

“ Five Factorial”

      5!  5  4  3  2 1  120
“ Seven Factorial”

      7!  7  6  5  4  3  2 1  5040
“ Zero Factorial”

      0!  1
Math Humor

Q: How can you tell when a factorial is enthusiastic?


A: It’s always enthusiastic – it has an exclamation
mark!



                      7!
Solve these expressions:

    6! 6  5  4  3  2  1
                            6
    5!   5  4  3  2 1

     8!      8! 8  7  6  5  4  3  2 1
              
  8  2 ! 6!      6  5  4  3  2 1

                     56
You try these:

     4!       4  3  2 1
                             24
     0!            1


     7!      7!   7  6  5  4  3  2 1
               
  (7  3)!   4!         4  3  2 1         !


                      210
 Permutation - Is a selection of a group of objects in which
                   order is important.


            n!
    nP 
      r
         (n  r )!

             
                  5!      5!   5  4  3  2 1
    5   P2                  
               (5  2)!   3!       3  2 1

                                          20
 Example 1:
  Flavio, Bruno, and Juanita are all going to meet at the
  Buena Park Mall. If they arrive one at a time, in how many
  possible orders could they arrive?

                   3     • 2 • 1
                                           = 6 different orders
                   1st     2nd     3rd
                 Arrival Arrival Arrival

          Permutation Method

                              3!      3!   3  2 1
             3   P3                    
                           (3  3)!   0!      1
                                                  6
 Example 2:
  How many cabinets of President, Vice President, Secretary,
  and Controller can be made from a group of 8 people?
               8      •    7      •    6     •      5
              Pres.       Vice        Sec.        Cont.
                          Pres.

                      = 1680 different ways

               Permutation Method

                     8!     8!                     8  7  6  5  4  3  2 1
     8   P4                                    
                  (8  4)! 4!                              4  3  2 1
                                             =      1680 different ways
 You try:
  How many ways can 5 surfers place 1st, 2nd and 3rd in a local
  surf competition?
            Fundamental Counting Principle
           5    •    4      •    3
         1st         2nd         3rd
                                        = 60 different ways
        Place       Place       Place

            Permutation Method

                    5!      5!            5  4  3  2 1
       P
     5 3                              
                 (5  3)!   2!                 2 1
                                        =   60 different ways
     HOMEWORK
WS Prob. I-4

				
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