More applications of permutations of non-distinguishable objects and introduction to combinations.

1. The difference between
Combinations and
Permutations
The Mastermind by jnthnhys
Combination (224365) by Cellach

2. Probability and Statistics

3. HOMEWORK
If 8 books are arranged on a shelf, what is the probability that 3 particular books
are together?

4. HOMEWORK
(a) In how many ways can the letters of the word GEOMETRY be 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?

5. HOMEWORK
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?

6. HOMEWORK
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?

7. 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?
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.

8. Combinations (the quot;Choosequot; Formula)
A combination is arrangement of objects On the calculator ...
where order does not matter. Press: [MATH]
n is the number of objects [<] (Prb)
available to be arranged [3] (nCr)
r is the number of objects that
are being arranged.
Examples:
How many different 5 person There are 15 people on the student council.
teams can be made from 10 How many 3 person subcommittees can be
people? made on the council?

9. There are 10 football teams in a certain conference. How many games must be
played if each team is to play every other team just once?

10. HOMEWORK
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 ...
Solve for the exact theoretical probability of
getting quot;at least 7quot; out of ten on this test.

11. HOMEWORK
(a) How many numbers of 5 different digits each can be formed from the digits
0, 1, 2, 3, 4, 5, 6?
(b) If one of these numbers is randomly selected, what is the probability
it is even?
(c) What is the probability it is divisible by 5?

12. HOMEWORK
Seven people reach a fork in a road. In how many ways can they continue
their walk so that 4 go one way and 3 the other?