This document provides information on permutations and factorials. It discusses how to calculate the number of arrangements of objects in different scenarios, such as arranging books on a shelf or seating people in a line. Formulas are given for permutations when objects are distinguishable or indistinguishable. Examples are provided to demonstrate calculating permutations for arrangements of letters in words or types of cookies.

2. In how many ways can 8 books be arranged on a shelf, if 3 particular
books must be together?

3. In how many ways can 5 people be seated in a straight line?

4. 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.
For example:
6! means 6 x 5 x 4 x 3 x 2 x 1 = 720
On the calculator ...
Press: [MATH]
4! = 4 x 3 x 2 x 1 = 24 [<] (Prb)
[4] (!)
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 3 628 800
1! = 1
By definition 0! = 1

5. How many ways can 8 different CD's be arranged?

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

7. In how many ways can you arrange the letters in the word HEEL
H E E L
H E E L
H EE L
H E LE
H E L E
H LE E
H L E E

8. Permutations of non­distinguishable objects ...
The number of ways to arrange n objects that contain k , k , k 3, ... sets of
1
2
non­distinguishable objects is given by:
Examples:
Find the number of different "words" that can be made by rearranging
the letters in the word:
(a) BOOK (b) MISSISSIPPI

9. How many ways can you arrange the letters in the word
REFERENCE
7560

10. If there are eight cookies (4 chocolate chip, 2 oatmeal, and 2 420
chocolate) in how many different orders can you eat all of them?

11. There are 10 people in a competition.
How many ways can the top three be ordered?
n Pr