Fundamental Counting Principle If two choices happen in
different ways, one choice is which pants to wear (called p ways),
another choice is which shirt to wear (called s ways), the number
of choices are p times s. If you wanted to include what type shoes
( called g), you would have p times s times g choices
Slide 3
Passwords If a password must contain one number and must have
seven letters. How many different choices are there? __ __ __
__
Slide 4
Passwords If a password must contain one number and must have
seven letters. How many different choices are there? 26 26 26 26 26
26 26 10 = 8.03 X 10 10
Slide 5
Permutations Permutation is the act of changing the arrangement
of a given number of elements. A,B,CA,C,B B,A,CB,C,A
C,A,BC,B,A
Slide 6
Permutations How many different ways in which to arrange 5
books? 1 st book, we have 5 choices 2 nd book, we have 4 choices 3
rd book, we have 3 choices 4 th book, we have 2 choices 5 th book,
we have 1 choice By the Fundamental Counting Principle how many
choices? 5 4 3 2 1= 5! = 120
Slide 7
Permutations The number of Permutations of n items is n! If
there are n = 7 choices of toppings on a pizza, how many pizzas can
be made? 7! =5040
Slide 8
Permutation when only wanting a limited number. 8 boxes of
cereal but only have shelf space for 3 boxes. 1 st space 8 choices
2 nd space 7 choices 3 rd space 6 choices Fundamental Counting
Principle 8 7 6 = 336 choices
Slide 9
Permutation when only wanting a limited number. Permutations of
n elements taken r at a time.
Slide 10
Permutation when only wanting a limited number. Permutations of
n elements taken r at a time.
Slide 11
What if you where looking at arranging the letters in race car.
How many different permutations. Remember race car is a palindrome
(same read from left to right or right to left). There are 7
letters with 3 repeating letters a, c and r.
Slide 12
Distinguishable Permutations race car
Slide 13
Combinations Here order is not important, in other words A,B,C
and B,C,A are the same because they have the same letters.
Slide 14
Given 5 boxes, how many combinations can there be of 3 boxes?
Box A, B, C, D, E {A,B,C} : {B,C,D} : {C,D,E} {A,B,D} : {B,C,E}
{A,B,E} : {B,D,E} {A,C,D} : {A,C,E} :10 combinations {A,D,E} :
