Design an experiment using coins to simulate a 10
question true/false test. What is the experimental
probability of scoring at least 70% on the test if
you guess each answer?
randBin(# of trials, probability of success, # of experiments)
How would you use your calculator to answer this question?
On the calculator ...
Press: [MATH]
[<] (Prb)
[7] (randBin)
How would you use Random.org to answer this question?
http://www.random.org/

The Fundamental Principal of Counting
If there are M ways to do a first thing and N ways to do a second thing then there are M x N ways to do
both things.
Example: Any one of 4 ties can be matched with any one of 3 shirts, How many
shirt and tie combinations are possible?
What if there are also 2 different pairs of pants that can be matched with all the shirts and ties,
how many different "outfits" are possible now?

Now you try ...
1) How many four-digit even numbers are there if the same digit cannot be used
twice?
2)(a) The last part of your telephone number contains four digits. How
many such four-digit numbers are there?
How many such four-digit numbers are there if the same digit
b)
cannot be used twice?

c) How many four-digit numbers begin with a 2 ,4 or 0 if the same
digit cannot be used twice?

How many ways can the letters of the word FERMAT be arranged?
Factorial Notation
When we want to multiply all the natural numbers from a particular number down to 1, we can
use factorial notation to indicate this operation. The symbol "!" is used to indicate factorial.
This notation can save us the trouble of writing a long list of numbers.
DICTIONARY
For example:
On the calculator ...
6! means 6 x 5 x 4 x 3 x 2 x 1 = 720
Press: [MATH]
4! = 4 x 3 x 2 x 1 = 24
[<] (Prb)
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3 628 800
[4] (!)
1! = 1
By definition 0! = 1

DICTIONARY
Permutations (the "Pick" Formula)
A permutation is an ordered arrangement of objects.
On the calculator ...
Press: [MATH]
n is the number of objects available to [<] (Prb)
be arranged r is the number of objects [2] (nPr)
that are being arranged.
Examples:
In how many ways can 5 people In how many ways can six students
be seated in a straight line? be seated in 8 vacant seats?

Permutations of non-distinguishable objects ...
The number of ways to arrange n objects that contain k,
k2, k3, ... sets of non-distinguishable objects is given by:
Examples:
Find the number of different "words" that can be
made by rearranging the letters in the word:
(b) MISSISSIPPI
(a) BOOK

Suppose that, when you go home from school, you like to take as great a variety of routes as possible,
and that you are equally likely to take any possible route. You will walk only east or south.
1. How many ways can you go from
the school to home?
2. What is the probability that you will walk
past the post office on your way home?

Design an experiment using coins to simulate a 10
question true/false test. What is the experimental
probability of scoring at least 70% on the test if
you guess each answer?
Let's think about this again using what we've just learned ...
Homework
Solve for the exact theoretical probability of
getting "at least 7" out of ten on this test.