This document discusses counting principles and probability through a series of word problems and diagrams. It asks the reader to determine the number of possible routes, paths, or outcomes in scenarios involving traveling routes, arranging letters, flipping coins, and a ball bouncing in a diagram. It aims to illustrate fundamental counting principles and calculating theoretical probabilities.

1. quot;How many meals?quot;
or
The Fundamental
Principle of Counting
Strange things on
the menu here by
flickr user leunix

2. Pascal's Triangle
How many different patterns can you find in the triangle?

4. Suppose that, when you go to school from home, 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.
(a) How many ways can you go to
the post office?
(b) How many ways can you go to
school?
(c) What is the probability that you will walk past the post office on
your way to school?

5. How many ways can the word RIVER be found in the array of letters shown
to the right if you start from the top R and move diagonally down to the
bottom R?
R
I I
V V
V
E
E
R

6. 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?

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

8. Find the theoretical probability of flipping three pennies and getting
at least 1 heads.
HOMEWORK

9. 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.
HOMEWORK