# Drink

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```					                 Lunch Specials

“Choose 1 Entrée, 2 Side Dishes and a Drink”
Entrée                              Side Dish
• 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:

 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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