Review of pathways problems, understanding the randBin() command on the TI-83 calculator and introduction to the Fundamental Principle of Counting and permutations.

1. Long Night
True or False
probability

2. HOMEWORK
A water main broke in our
neighborhood today. My kids
want to get to the park to play as
quickly as they can so we only
walk South or East. How many
different quot;shortest pathsquot; are there
from our house to the park
walking on the sidewalks along
the streets?

3. HOMEWORK
The diagram below shows a game of chance where a ball is dropped as indicated,
and eventually comes to rest in one of the four locations labelled A, B, C, or D.
The ball is equally likely to go left or right each time it strikes a triangle. We
want to determine the theoretical probability of a ball landing in any one of these
four locations. To do this, we need to know the total number of paths the ball can
take, and also the number of paths to each location.

4. HOMEWORK How many ways can the word
quot;MATHEMATICSquot; appear in the
following array if you must spell
the word in proper order?

5. 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/

6. Find the probability of flipping three pennies and getting at least 1 heads.

8. quot;How many ways?quot;
or
The Fundamental
Principle of Counting
Love can be in many flavours

9. The cafeteria special for lunch offers a choice between two main courses
(hamburgers or chicken burgers) and three different drinks. The quot;meal dealquot;
allows you to pick one of each. How many different quot;meal dealsquot; are they
offering?
What if they offer to throw a choice of fries, spicy fries or plain chips. How
many quot;meal dealsquot; are they offering now?

10. 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 quot;outfitsquot; are possible now?

11. Now you try ...
How many four-digit numbers are there if the same digit cannot be used twice?
How many four-digit numbers are there if the same digit can be repeated?

12. How many four-digit even numbers are there if the same digit cannot be used twice?

13. HOMEWORK
(a) The last part of your telephone number contains four digits. How
many such four-digit numbers are there?
b) How many such four-digit numbers are there if the same digit
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?

14. HOMEWORK
How many ways can the letters of the word FERMAT be arranged?