Introduction to combinations and the connection with permutations of non-distinguishable objects.

1. In Today's Class:
Why they never should have called this a combination lock.
royal combination by
flickr user Darwin Bell

2. Permutations of non-distinguishable objects ...
The number of ways to arrange n objects that contain k1, k , k 3, ... sets of
2
non-distinguishable objects is given by:
Examples:
Find the number of different quot;wordsquot; that can be made by rearranging
the letters in the word:
(a) BOOK (b) MISSISSIPPI

3. If a fair coin is tossed 4 times, what is the probability of obtaining
exactly 2 heads?

5. If a fair coin is tossed 4 times, what is the probability of obtaining
exactly 2 heads?

6. If a fair coin is tossed 4 times, what is the probability of obtaining
exactly 2 heads?

7. All the letters of the word MANITOBA are arranged at random in a
HOMEWORK
row. How many ways can this be done?
How many arrangements will have the two A’s next to each other?
What is the probability that this random arrangement will have the two
A’s next to each other?

8. (a) In how many ways can the letters of the word GEOMETRY be
HOMEWORK
arranged so that vowels and consonants alternate?
(b) In how many of these ways is Y the last letter?
(c) If one of these quot;wordsquot; is randomly selected, what is the probability
that Y is the last letter?

9. 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.
How many ways can you
go from the school to
home?
What is the probability that you will walk past the post
office on your way home?

10. 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.
How many ways can you
go from the school to
home?
What is the probability that you will walk past the post
office on your way home?

11. 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.
How many ways can you
go from the school to
home?
What is the probability that you will walk past the post
office on your way home?

12. Design an experiment using coins to
simulate a 10 question true/false test.
What is the experimental probability of
scoring exactly 70% on the test if you
guess each answer?
HOMEWORK
Solve for the exact
theoretical probability of
getting quot;at least 7quot; out of
ten on this test.

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

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